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).
Thor is holding his hammer in his right hand while he comes to the Bifrost and confronts Loki. When Loki sends him flying and he falls on his back and his hammer hits the floor, the hammer is in his left hand. It's back in his right hand after he gets up.
During the fight scene on Jotunheim, Loki's Left arm is grabbed by one of the Jotuns and his glove / clothing / armor disintegrate away to this touch revealing Loki's Jotun heritage. But for the rest of the scene he appears to have regained both glove, clothing and armor as his hand and arm are clothed again.
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 scene inside the agent's car still standing up on the dashboard.
When Jane, Erik and Darcy are on the roof of the garage after SHIELD has taken Jane's stuff, there is wind in their hair in the shot from one angle and no wind in the same scene shot from another angle.
The goof items below may give away important plot points.
When Loki is on his way to the Bifrost on horseback to destroy Jotunheim, he is wearing his helmet. As he is actually activating the Bifrost, his helmet is absent. The scene cuts to the Bifrost destroying Jotunheim for a few seconds before reverting back to the Bifrost interior where Loki is once again wearing his helmet, presumably just removing his staff from the activation.
After the destruction of the Bifrost, Loki is dangling from his staff that is held by Thor. Loki is gripping the staff at least 3 feet from the bottom. As the discussion continues you can still see that his hand has not changed position but at the very last just before he makes the decision to fall he is only gripping it about 4 inches from the bottom.
Jane is considerably shorter than Thor. Near the end, they are talking and she has to look up at him. When they kiss, she is suddenly at eye level. If you watch the horizon behind them though, you can clearly see that this is because the camera is tilted and Thor is bending down.