John Connor is seen driving a JK series 4 door Jeep Wrangler, which was first manufactured in 2007. Skynet launched its massive nuclear war, destroying most of humanity, in 2004. There wouldn't be any new vehicles after that.
When Blair and Barnes are both standing in front of Marcus while he's hanging, Blair takes Barnes' pistol and shoots Marcus. The sound of the gun firing and the muzzle flash do not happen at the same time like they should.
After pursuing Marcus Wright to the river after he escapes, Connor's helicopter is attacked by Hydrobots. As one of the machines breaks through the Helicopters frontal control panel, we see the pilot fire at least four pistol rounds at the machine, yet no gunshots are heard.
Airborne targets that have not been identified as hostile, friendly or neutral are called bogies. Targets that have been confirmed hostile are called bandits. An A-10 pilot called the prisoner transport and the HK a bogie yet they were already identified as enemy (hostile) aircraft.
When Marcus rescues Blair from the gang shortly after they meet up at first, it's dark and pouring down heavily. Right after Marcus somehow manages to find dry wood to burn, the ground and everything around them is completely dry.
When Blair drops the shackled Marcus, he's in an upright position, leaning slightly forward, and he falls straight down. He should have landed upright and fallen on his face. However, when he reaches the bottom (a drop of no more than 20 feet), he's in a prone position and lands on his back.
In the opening execution scene, there are six loaded syringes in a row, all extended. Syringe five descends first, and in this shot syringe three is returning to its fully extended position, when previously it was already extended. Then syringe three descends again.
When Marcus and Kyle have found their first abandoned vehicle and just got it started, they are all inside and the windscreen is covered in mud or dust which means it's going to be pretty difficult to see out. However, as they are attacked and have to drive off in an instant, the windscreen (seen from the outside) is suddenly crystal clear.
When John Connor takes off on the chopper in the beginning of the movie, he never put on his safety restraints. He never removes his hands from the controls so he could not put it on in flight. After he crashes upside down, he is held in his seat upside down by the belt he never put on.
When Marcus is repairing the jeep and they start driving away he doesn't clamp down the hood with the two hood latches on the outside of the hood. Yet while they are escaping the hunter killer you can see the two hood latches secured in place.
When John, Kyle, and Star enter the T-800 manufacturing facility we see several T-800 skulls. The skulls already have the brightly lit red eyes placed into the eye sockets. When the camera cuts in the next picture we see an assembly arm install eyes into the eye sockets of one of the skulls.
During the confrontation in the 7-Eleven between Kyle Reese and the resistance fighters, forward shots of Reese show him protecting Star with his shotgun, while close-ups and over-the-shoulder shots have Reese pointing the weapon at the lead resistance fighter ("If you're going to point a gun, you'd better be ready to pull the trigger.")
When Marcus Wright learns how and why he was programmed he throws a table at the see-through screen. A wire attached to the table can be seen suspended from it as it comes to rest, essentially hanging in the air.
During the opening attack on the Skynet facility, there is a POV shot of a missile heading towards a target at North 36 deg, 17 mins, 22 secs and East 117 deg, 15 mins, 23 secs. Those coordinates are in Eastern China, south of Beijing, an unlikely target for Connor's team to travel to. However, if the eastern coordinate of 117 deg is changed to West then the target is in Death Valley, California, a more probable target.
In the past three movies, it's been explained over and over that John Connor was the leader of the resistance. In this movie, not only is he not the resistance leader, but he's not even a part of the senior command group. There is still some time to go in the story before he becomes leader.
John Connor knows his father's name only from the records his mother left him. It is not made entirely clear how Skynet could have obtained that information too and how it can identify Kyle Reese by his face (something which is not known even to John). However, it's entirely plausible, given Skynet's access to global information, that it could have obtained such information from records of events shown in previous Terminator films, such as Kyle Reese's arrest record and subsequent filmed interview in The Terminator; this would have given Skynet a picture of his face, which could then be used in conjunction with facial recognition software to identify him. Additionally, during the many interviews between Dr. Silberman and Sarah Connor in the mental institution shown in Terminator 2: Judgment Day, Sarah Connor very openly talks about Kyle Reese and his role in future and past events. Between Kyle Reese's arrest records and Sarah Connor's medical records, Skynet would have all the information it needed.
Kyle states that traveling at night would be difficult because Hunter/Killers have IR sensors and would detect body heat, yet Blair starts a fairly large fire out in the open at night without any concern. However, these are two different characters with two different levels of experience with Skynet (and its terminators). Also, fire does not necessarily mean a human is present or near and may even mask body heat.
In the first The Terminator, Kyle Reese explains to Sarah that he was born in the camps and bred as a soldier of the resistance. In Salvation, we can clearly see that he was just an ordinary civilian survivor of the war and did not become an actual resistance soldier until he was a young man. This is not necessarily a goof. He could have been exaggerating to impress her in the first movie. Alternately, the time travels of the sequels could have changed the events of his early life.
Dr. Serena Kogan is seen without head hair as a result of cancer treatment, but she still has her eyebrows which would have also been lost. However, since cancer patients react differently, she may have kept her eyebrows. (Hair on your head falls out quickly - facial hair does not always fall out.)
When John and other resistance members are testing the short-wave radio code on a captured Hydrobot, he asks the technician to "turn it up". She turns up a dial marked "Coarse". That indicates that she is adjusting a frequency, such as produced by a signal generator, rather than increasing the power or signal strength, which would be labeled as such. However it appears that the resistance fighters have had to "make do" with stuff and may have repaired the machine using what was available or retro-fit it with parts from another unit
When John Connor drives up from southern California and into San Francisco to enter Skynet, he drives across the Golden Gate Bridge moving North to South from Marin County. Though it seems more logical for Connor to approach SkyNet from the south, he may have chosen a northern approach because SkyNet may have installed heavier defenses to the south, anticipating an attack by the Resistance. Connor would have known that fact and could have taken the long route around the San Francisco region to avoid those defenses.
The photo of Sarah Connor in this film uses a portrait layout and is cropped differently from the landscape framed photo in The Terminator. The photograph could have been copied several times over the years.
When John Connor uses a radio playing Guns N' Roses "You Could Be Mine" to attract a motorbike-terminator, the music stops when he catches it. However, the radio can be seen intact in the road and Connor does not switch it off. The moto-terminator could have some carrier wave to disrupt the power of the radio.
During the motorbike chase scene, the road has double yellow striping. Later, before the bike and camper van approach the bridge the striping changes to a white lane-divider line. White center striping on US roads was replaced with yellow in the 1970s, but this could be a backwater that never got the new colors.
When Blair is hanging suspended by her parachute tangled in a tower, she asks Marcus to hand her her knife to cut herself down, and then proceeds to cut her way through her right parachute riser, after which she falls free. She ignores the canopy release on her shoulder (designed to release the parachute in less than a second. However the left side has already been released (and she did not have the knife to cut it yet). Any fighter pilot has to use both releases every time they fly, once to attach to the parachute (which is packed into the ejection seat, not worn), and then to release it again to exit the aircraft, so it is incomprehensible that they would not know how to release it properly.It may be possible, however, that the release was jammed or damaged.
The Resistance planned to end the war using a signal to disrupt the terminators communication with their central command. John Conner should have known this plan would fail as he had already witnessed several terminators continue to operate after having been cut off when they traveled back in time in the previous movies.
There is no reason for Skynet Central to have touch screen interfaces as used by John Connor. The machines should be able to communicate directly with any equipment they need to use and most terminators up to that point lack the fine coordination to operate a touch screen.
When Marcus starts the car and the music starts playing, the street lamp posts still have their glass bulb covers intact. Considering all the cars had either had their windows blown out or were charred, the streetlamps would have suffered a similar fate in the event of a nuclear blast.
In the first big battle scene, a number of members of "The Resistance" leave their helicopters after they land. But as they are walking/running from the helicopters, their hair (especially the woman with long hair) is blowing toward the helicopters, not away from it.
During the motorbike chase sequence after the ball on the end of the tow truck snags the terminator and starts dragging it and just before the truck goes over the bridge, you can see the drag lines made on the right side of the road during principle photography for the animators to add in the CG ball, cable, and bike in post.
In the first battle scene, specially when Connor took over the helicopter and tried to pursue the enemy's ship, after the blast and when the helicopter started to sway and fall, at some moments we can see the top glass roofs of the cockpit are still green, revealing that the whole scene was shot in a green screen studio.
The goof items below may give away important plot points.
John Connor says that the power cells, used to blow up the Skynet base, are for the T-800, which is in fact false. The power cells were created for the T-850, seen in Terminator 3: Rise of the Machines. If those particular power cells were used in the T-800, the terminators from The Terminator and Terminator 2: Judgment Day would have ended in a catastrophic explosion after being crushed in part one and melted in molten metal in part two.
When John Connor is carried to the helicopter after the final fight scene, he is helped into a helicopter and laid right next to the older lady (Virginia), who then disappears from the subsequent helicopter scenes.
In the final scenes after Marcus smashes the display screen, he exits the control room, In the background is gunfire-marked paneling. During the next scene, the Terminator has Kyle on a table being put into a machine. The gun fight takes places and the currently unmarked paneling gets shot up.
It is clear that the marks created from the gun fight are the same as the marks behind Marcus from the earlier scene. The plot locations are supposedly different, so the scenery was obviously reused but gunfight scene must have taken place before the scene with Marcus. As no fighting had taken place near the control room, the paneling behind Marcus should have been unscathed.
When John is lying on the ground in the factory as the terminator bears down on him, the terminator appears to be right beside him but when he shoots the part to release the hot fluid to land on the terminator, the terminator then is suddenly farther away from John.
When Connor blows up the Skynet factory the explosion is nuclear. The chopper they were all flying in would not have made it out as it is electronic, and nuclear detonations produce extreme amounts of electro-magnetic radiation. One might argue that the chopper was out-fitted to resist that sort of radiation, but the fuselage was open so even if the craft itself wasn't hurt the passengers all would have been contaminated with radiation poisoning.
The machines can hear rock music from miles away, but are incapable of hearing two low-flying jet fighters. However, the statement that the robots heard the rock music was simply a guess as to how the robots located them. We know that Skynet is actively looking for Kyle Reese and later we see that everything Marcus observes is being monitored, so Skynet already knew exactly where to go.
When Marcus first enters the City (Los-Angeles), he calls to a man in the distance who turns out to be Terminator, that then begins shooting at him. This makes sense because SkyNet had to maintain Marcus's cover as an ordinary human (and also explains the Terminator's terrible aim). It's later revealed Marcus is also a Terminator and SkyNet's machines identify him as a friendly because as far as SkyNet was concerned, Marcus had completed his mission and was coming "home".
John Connor gets a heart transplant in the middle of the desert, and apparently with out medical tools. Even more, Marcus' heart is compatible with that of John's. However, we know that Marcus's human tissue has already been altered. After he gets blown up by the mine and is being examined medically it is stated that his flesh is human but heals much faster than normal. Obviously his human flesh has been changed by Skynet using futuristic technology. It is conceivable that it therefore doesn't have compatibility problems and that John will heal really quickly with the altered heart inside him, even in the middle of the desert.
Marcus quickly and skilfully repairs a broken radio and a disabled Jeep. While some would think this is a subtle indication of Marcus being a Terminator, nothing about his background is ever revealed beyond how he wound up in prison. It's possible he learned those skills naturally.