(at around 1h 21 mins) The coffee cup on the dashboard in the SHIELD agent's car is knocked over by the vibration of the Destroyer's arrival, in the next few shots of the same scene the coffee cup can clearly be seen inside the agent's car still standing up on the dashboard.
(at around 37 mins) In the Healing Room when Loki is shown re-examining his left hand, the edge of his sleeve is brown instead of the green of his attire, as seen immediately after.
(at around 52 mins) When Jane and Thor are going to the crater, there are wired fences visible on the side of the road. When the camera cuts to an outside shot of the car, the fences are gone.
(at around 43 mins) The hammer landed about 50 miles to the west of the town (according to the man in the diner). When Sif and Co. arrive, the SHIELD agent at the console says that it was about 50 miles to the north-west (at around 1h 17 mins), placing it 75-80 miles from the town. Yet, when the Destroyer arrived, which was at the same location as Sif and Co, it was clearly on the outskirts of town.
(at around 1h) Thor is soaked and covered with mud when he drops down in front of the hammer in the SHIELD enclosure. When he is led away by the guards, the shot is of a very clean man in a clean navy blue top.
While Odin is still alive and Loki is a king in his stead, he is called "King." He would only be King once Odin dies, until then he would be "Prince Regent."
(At about 43 mins) When Thor learns of where Mjölnir landed (50 miles west), he is seen leaving the diner, and most likely heading east. It seems to be around mid day when looking at the shadows cast by the characters, they're pointing north, which should have Thor walking away from the camera, instead of towards it.
When Coulson calls for eyes up high, Barton grabs a bow and throws it into the basket hanging from the crane before climbing in himself. No real expert bowman would ever mistreat his equipment like that.
Irritating as h that the king of the frost giants is named Laufey a female name.
Thor can summon Mjölnir from a distance but he couldn't summon it when he was in the town -- at least, he isn't seen trying what he should've instinctively done -- therefore, he should've known he couldn't pick it up from the crater. The Asgardians are shown to be psychologically very similar to humans and Thor was, essentially, human at this point, so, he very naturally tried to lift it, even knowing he would fail. Furthermore, Thor knew he had been stripped of his powers by Odin, it's very likely he would expect Mjolnir's touch from his worthy hand to be enough to reunite them.
When the hammer, racing towards Thor breaks the sound barrier, you hear the thump before the hammer arrives. Not going to happen. Sight (light very fast) then hammer, last the sound arrives. However, in this case, the sonic boom heard in town was from the hammer breaking the sound barrier as it rose into the sky. With the arcing path it takes to get to Thor, there is more than enough time for a sonic boom to reach them first. There should have been a devastating boom immediately after the hammer arrived though. It would have shattered every window and likely deafened or stunned those nearby.
(at around 43 mins) When Thor leaves the diner heading to the crater site, the street is wet. There's no evidence it's rained since Thor's arrival.
At the post-credit scene, when Selvig met Nick Fury, his patched eye did not have 3 lined scratches from Flerken that happened during Captain Marvel's event.
(at around 35 mins) When Darcy picks up her TASER X26 from her bag (right before Jane backs into Thor outside the hospital), the sound of a pistol slide being maneuvered is heard. The TASER X26 does not have a slide or any moving part that can replicate that sound. Also, Darcy only picks it up and turns it around before putting it back in her bag, she doesn't move anything (safety, cartridges, battery pack).
(at around 1h) When Thor is led away after getting cuffed (after his attempt to retrieve the hammer), it is obvious that there is only a white, plastic loop keeping his hands in place. Despite the fact that we have heard the sound of cuffs. The loop is also not tight enough to serve as cuffs; it only serves as help for the actor.
(at around 1h 24 mins) When Destroyer fires at Thor during the attack on the town, Thor rolls towards this left in the air to avoid the explosive next to him on the ground. Thor is wearing what appear to be black glasses, possibly to protect the stuntman's eyes from the flash of the explosive next to him.
(at around 51 mins) On a SHIELD monitor, "perimeter" is spelled "perimiter".
Barton is a Right-hand shooter. Just only in 'Thor' in the other movies, Barton is a Left-hand shooter.
When Thor makes a plea to his Loki, who is controlling the destroyer at the time, to take his life and spare the innocents, Loki accepts, has the destroyer swat Thor with a killing stroke then has the destroyer turn and walk away as if to be leaving peacefully. Loki could not do this and keep his usurped crown since Thor's 4 warrior companions are witness. Loki would need to kill the 4 warriors as well.