Dollarhyde gives a knife to young Emmett that he claims he obtained as a boy. The knife is obviously stainless steel. Stainless steel wasn't invented until 1904 and didn't become available to the public until decades after that.
When Jake is looking up through the hole in the roof of his house, there are two crossed boards held together by a screw with a recessed head. The square or Phillips headed screws were not invented until the early 1900s.
Sheriff John Taggart identifies himself as Emmett Taggart's maternal grandfather ("Your ma's buried here, and you know I don't want to leave my little girl."), and the boy's father is supposedly still alive. If so, then the Sheriff and Emmett should have different last names.
When Jake is riding towards his house, the scene is a long shot but it can be seen very obviously that the bracelet is missing from his arm. In the following shot the bracelet is suddenly back on his arm.
The three cowboys Lonergan meets after first waking up appear very dirty and sweaty, and all of their equipment is old and used. The cowboy hat he later takes from one of them is obviously new, as it doesn't appear dirty and doesn't have a sweat salt stain where it would rest on one's head.
After the first Alien attack at roughly 45:20 into the movie when Jake Lonergan rides after the Aliens on his own, his bracelet is seen missing for a few seconds until a close shot where the bracelet is back.
The morning after the first alien attack, the posse follows the trail left by the alien which, according to the dialog, headed North. However, the early morning shadows cast by the sun on the the riders and their horses are on their right, which indicates that they're riding Southward.
The Apache chief needs a translator to communicate with the cowboys, except in the scene where Ella tells them all who she is. In this scene, there are a few times when the Apaches appear to understand English.
When Jake encounters his old gang, he punches in the mouth the first guy that comes close and who had recognize him. He has blood on his finger in the next shot. A few shots later the blood vanishes and after several shots it reappears.
When Jake is riding his horse to rescue Ella who has been picked up by an alien ship, his horse changes three times. He starts on a light bay with a star. Then he is riding a bay without a star. Finally, when he is leaping from the horse onto the ship, he is riding yet a third horse, a very dark bay.
When meeting up with Jake's old gang in the valley, they are told to put their hands in the air. In one of the shots Ella is seen getting off her horse. In the next shot, immediately after the previous, she is standing beside her horse, but there is no way she could have gotten off her horse so quickly.
The energy used to travel the stars could have powered a machine to atomically create gold from other elements. Dr. Glenn Seaborg lead a team in 1980 which created gold from bismuth. Unfortunately the power and equipment costs far exceeded the value of the gold created.
Gold has been discovered by scientists in the composition of objects in outer space and most astronomers and astrophysicists believe that gold on Earth came to Earth via meteors. That means the aliens could have easily harvested gold while in space without having to use additional energy to extract it on Earth and then boost it into orbit.
When Woodrow and the rest of the men on the trail of the aliens arrive on horseback at the upturned boat, it is raining heavily. However, no rainwater appears to be dripping off the brims of the men's hats.
After the first alien attack it is stated that they will leave at first light, but the next morning from the length of the shadows on the ground it can be seen that the sun is up and it is well into the morning.
The goof items below may give away important plot points.
When Jake Lonergan and Colonel Woodrow Dolarhyde are escaping the alien stronghold, Jake is hit by a blast of dust as they emerge from the cave opening. In this shot, Jake is clearly covered by dust, however in the next shot, he is again clean.
Wrongly regarded as Continuity Error - It was stated that at the end of the movie Jake and Dolarhyde are talking when a horse and colt walk by in the background...a wagon passes by and the colt mysteriously disappears. This is not a Continuity Error, although it looks like it. In reality, the colt is trotting at a faster pace than the horse. Just before the wagon passes the camera, one can see that the colt is quickly passing the horse on the left, in an arc. By the time the wagon clears the scene, the colt is now directly in front of the horse, out of view from the camera's angle. But the viewer can (barely) make out the colt's legs moving in front of (and viewed through) the horse's legs. The colt did not disappear due to film editing.
Although Ella explicitly states that the aliens are blinded by bright light and avoid it, they later appear to have no problem fighting in full daylight nor do they appear to be inconvenienced in any way by it.