(at around 1 min) One dinosaur that's shown witnessing the great extinction event at the end of the Cretaceous is a Psittacosaurus. Psittacosaurus went extinct in the middle of the Cretaceous, around 40 million years before the end of the age of dinosaurs.
(at around 6 mins) When Cade first opens the door to the truck (Optimus Prime), he looks at the bullet casings that fall out and identifies them as "Mortar shells?" Mortar shells do not leave behind casings, and an intact mortar shell is not that shape, nor would it be made from brass.
(at around 49 mins) Shane says that the Romeo and Juliet law protecting his and Tessa's relationship states that they can be together as they were already together when Shane was a minor. This is only partially correct. Shane has a legitimate defense against "Sexual Assault" (Sec. 22.011) as Tessa has consented and is over the age of 17, and when they were dating when he was 17 and she was 14 there is an age difference of less than three years (provided Tessa turns 15 before Shane turns 18). However, the issue of their age difference, consent, prior relationship, and Tessa being 17 only applies to the crime of Sexual Assault. Romeo and Juliet laws do not protect him from the crime of "Sexual Performance by a Child" (Sec. 43.25) for engaging in "sexual contact, actual or simulated sexual intercourse" with Tessa. Here the relevant age to engage in sexual conduct is 18 (she is 17), and the difference in age must be less than 2 years (there's 3) for a legitimate defense against the crime.
(at around 2h 30 mins) In the Optimus/Lockdown fight when Cade hides behind the wall and Lockdown fires a round into the bit of wall right next to Cade all of a sudden someone in a grey suit is visible behind that wall for less than a second who instantly bursts into a cloud of red mist. He wasn't there in the shot before and no trace of him whatsoever can be seen afterwards.
(at around 41 mins) When the main characters are being chased through the cornfield by the CIA, a pursuing car hits them on the side, however in the next shot the car has disappeared and the main characters car has not lost any speed.
(at around 9 mins) When Optimus is being towed to Cade's property, there is a shot of Cade turning on to the road leading up to his house with the sun is setting in the backdrop. The next shot of him arriving at the house still towing Optimus it appears to be midday.
(at around 1h 21 mins) When Tessa gets into the white car that Optimus is laying on, she shuts the door. The camera changes a couple times. When it shows Optimus from the outside, the door is open, and when it pans back to Tessa, the door is closed again.
(at around 1h 55 mins) During the Hong Kong chase, right after Joshua Joyce says 'death is on our tail', there is a Cadillac right behind them. In the next shot, when they ride around a corner, the Cadillac has suddenly changed into an Audi.
(at around 1h 13 mins) When the Autobots storm KSI and Hound is shooting off his gun, the security guards do not all react at the same time. People start running while security guards are still standing still and facing forward.
(at around 2h 30 mins) When Cade is firing at Lockdown, he moves from a wall with the remains of a circular opening to a squared shaped piece of wall/concrete. In the next shot he is back behind the wall with the square in the distance.
(at around 1h 45 mins) While the Autobots are in the train yard, Drift says that Joshua Joyce is heading to Guangzhou, China. However, when Joyce is shown arriving in China, text on the screens says 'Beijing, China'.
(at around 1h 50 mins) From the start of the movie, Tessa is wearing jeans up to the train/wagon scene. Just when the police cars appear, she enters the spaceship wearing camo-pants and a belt up to the end of the movie.
(at around 51 mins) Over the course of 3 minutes the clothing of all 3 primary actors changes 4 times from when they're at the souvenir shop to when they meet the other Autobots. Cade goes from a gingham shirt and hat to a plaid shirt and hat to no hat and a brown leather jacket over a long sleeved gray shirt to white tee. Tessa changes from jeans and a long sleeved white shirt to shorts and a patterned tee to jeans and a white jacket then to jeans and a white 3/4 sleeve shirt. Shane goes from a green Henley to a gray tee to a black leather jacket over the gray tee to a gray hoodie.
(at around 1h 6 mins) When Cade, Shane and Bumblebee break into KSI labs, Bee hits Shane in the face (as a car) and he falls on the ground beside Bee. When Bee drives around a second later, Shane has disappeared. He reappears in the next scene.
(at around 1h 55 mins) In China, the main characters drive from Beijing to Hong Kong in one evening. The two cities are 1,504 miles apart (Source: Bing Maps). It is literally impossible to do that in real time. It would take 22hrs to drive that distance by car (including traffic).
(at around 2h 25 mins) In many scenes on Hong Kong island, characters talk about reaching "the bridge" to escape, but the main Hong Kong island is not connected to the continent by any bridge, only tunnels. The large bridge featured later in the movie connects the continent to another island (Lantau).
(at around 2h 10 mins) In one of the fight scenes in Hong Kong, an Amercian-style yellow traffic light is hanging by wires. Hong Kong, being an ex British colony, used and continue to use United Kingdom-style traffic lights.
The fight scenes in Hong Kong jump all over the place. In one scene Optimus Prime is fighting simultaneously in different parts of Hong Kong Island (Causeway Bay, Central and Admiralty) and also Kowloon, on the other side of Victoria Harbour.
(at around 2h 30 mins) During a fight scene in Hong Kong, the Willis Tower is visible in the background between two buildings. Next to it is what appears to be 311 S Wacker, the building next to the Willis Tower in Chicago.
(at around 1h 55 mins) When Joshua and his associate Su Yueming flee from Beijing to Hong Kong, their car still carries mainland China 'Blue Plates', along with their pursuers' vehicles as they enter the city. By law, any vehicles entering Hong Kong from mainland China must also carry a pair of Hong Kong license plates with the prefixes 'FU' or 'FV' in the standard white/yellow plate scheme with their original Chinese plates. All the cars from China are carrying plates from Shenzhen, not Beijing, even though they drove to Hong Kong from Beijing.
(at around 3 mins) The remains of Tyrannosaurus and Spinosaurus can be found together at the arctic dig-site. This would be impossible, since not only did they live tens of millions of years apart, Tyrannosaurus lived in North America while Spinosaurus lived in Africa.
(at around 2 mins) The initial scene is supposed to happen in 'the arctic' yet it appears to be a surface mining site with rock cliffs. The arctic is a layer of ice on top of an ocean. There is no rock ground to dig there.
(at around 1h 18 mins) During the chase sequence when Optimus and Galvatron fight for the first time a road sign for South M 52, the highway in Michigan where the scene was filmed, is visible. The storyline indicates this takes place in Illinois.
(at around 13 mins) It's stated early in the movie that Cade lives in Paris, Texas. In one scene the real estate lady has phone number on car with a 512 area code. 512 is the area code for Austin, 300 miles away from Paris. The Paris, Texas area code is 903.
(at around 58 mins) At the dig site, the find was said to have been carbon dated to 65 million years. This is not possible, because carbon dating does not work on samples this old. Also the sample was said to be metal, which can't be carbon dated regardless of age.
(at around 1h 6 mins) When Bumblebee does doughnuts in the KSI building, one of the villains states that the they "Don't scan collector car junk". However, there is a vintage Corvette stingray race car seen just prior to this. So obviously they do scan collector car junk.
(at around 2h 35 mins) A Mercedes-Benz police van representing the Hong Kong Police SWAT (HKP-SWAT) can be seen at Victoria Harbour where the Autobots gather with the police. The tactical unit of HKG is in fact known as the Special Duties Unit (SDU) and have always being plain navy blue with simple "POLICE" marking and use a Mercedes-Benz Unimog U5000 for armored personnel carrier, not a 814D. Due to their secretive nature, unlike other tactical units, they never carry out operations without wearing balaclavas.
(at around 2h 5 mins) In Hong Kong, when Cade, Joshua, Tessa, and Shane enter the elevator to run away from the rooftop, the elevator won't move and Cade says it is overloaded. But in the next scene, we could see that the maximum amount of person that the elevator could bring is 9 people. There are only 4 people and the seed (the seed is not as heavy as human because Joshua could lift it easily).
(at around 36 mins) When the CIA is looking for Prime on the Yeager farm, a 30+ foot hole under the barn becomes available for Prime to hide in and even though the CIA team has technology to see through walls as demonstrated earlier in the movie when they capture the Autobot on the riverboat, they cannot detect Prime through a few wooden slates that are spaced enough to see through with the naked eye.
In previous installments, Energon detection was supposed to be the way Transformers could be easily tracked and spotted, yet in multiple instances in this movie the technology seems to have been lost: by the squad team in the barn where Prime was being repaired, or earlier when Lockdown is obviously using infrared vision to track Ratchet.
(at around 1h 17 mins) When Galvatron and Optimus fight, Optimus and Bumblebee save the people, and then Optimus and Galvatron resume fighting. The other Autobots should join the fight, but they are not anywhere near.
(at around 1h 3 mins) Somehow, taking a picture of a random employees badge gives Cade unrestricted access to the entire KSI building including the Top Secret labs and access to the head of the company and top scientists. There is no way that a picture of the front of a card would give swipe access to any areas as the access is coded on a strip or chip in the card and is not visible.
(at around 1h 45 mins) Right before KSI's move to China, a technician can be seen in the background working on Galvatron's truck form. But Galvatron is made of "transformium" and can be turned into anything. No technicians are needed.
(at around 15 mins) During the fight on the boat near the beginning of the movie, the covert ops team commander is watching the action on his monitors. Many of the monitors are green indicating they will have content added in post-production. There is no logical reason for them to be green, they would either be off, on with images, or on a standby mode. The content was never added. We see this a few times.
(at around 1h 18 mins) Several times the human characters fall or are thrown several feet without any injuries. During the highway chase scene where Prime fights Galvatron for the first time, Tessa rolls along the concrete highway at highway speeds but then gets up without a scratch. During this same scene, the humans are thrown in the air through fire and "caught" by metal robots without a scratch.
(at around 2h 5 mins) During the fight/chase along the rooftops and down the side of buildings in Hong Kong an air conditioner unit is pulled off the wall and dropped on Cade. The wall was left completely blank showing that it was not a real unit as there was no window or any access through the wall for air to flow nor were there any wires or piping.
(at around 2h 15 mins) As the camera passes through the room that Cade, Joshua, Tessa, and Shane are hiding in just before Hound says, "I'm a fat ballerina," the window frame on the right disappears - suggesting it wasn't real but a computer generated image.
(at around 1h 17 mins) During first encounter with Galvatron, when the semi jack knifes in the middle of the road you see aluminum cans flying out of the containers (they word of had a tarp or netting covering it). The way it jack knifed looks fake and the RV it hit was employ with no driver.
The goof items below may give away important plot points.
(at around 2h 5 mins) In Cade's fight with James Savoy, Cade gouges James's eye out with his thumb and throws him to the ground. When James stands back up, his eye is perfectly fine. For the rest of James' scenes in the film, no reference is ever made to any eye injury.
(at around 2h 30 mins) In the final scene in Hong Kong where Shane and Tessa are trying to free Optimus from being impaled to the wall with the tow truck, the exact shot of Tessa running to pick up the hook, you can clearly see the Willis (Sears) Tower in Chicago in the background.