Other mistake: Each time Cage is on the dropship along with all the other soldiers, the dropship is attacked and all the other soldiers release themselves from the plane onto the beach. When Cage lands on the beach, note the area he is standing in. Every time he drops onto the beach, he releases himself earlier or later than the previous time, but despite this, he always seems to land on the beach in the precise same spot each time. The dropship was attacked and began spinning out of control and was not in a fixed position, so there is no chance he would have landed in the same spot even if the dropship was over the same location.
Suggested correction: I don't think you're right, because the dropship doesn't change its rotation or acceleration, Cage just is connected longer or shorter to the ship, depending on the time when he chooses to let him self fall. It would be possible for him to land on almost the exact spot every time he cuts the rope to the ship.
I'm not sure this correction makes sense. If Cage was connected to the ship for a longer or shorter time, then he'd have traveled a longer or shorter distance. Then he'd land in a different place depending on how far he'd traveled. It would be almost impossible for him to land in the same spot each time.
Other mistake: In the landing scene inside the dropship there is a release valve for all the mechanical suits. No one seems to use this valve to get released, they all just drop spontaneously. Except for Cage, who has to hit the valve every time in order to get released. (00:18:50 - 00:33:04)
Suggested correction: They all wait until they are released automatically. Probably deploys at a certain distance from the beach.
I'm not sure this answers the mistake. There's no apparent reason for deployment to be automatic for everyone except Cage. It could be argued that everyone else knew to select "automatic drop," but Cage didn't. However, since that's not covered in the film, it can't be used to explain what happened.
Well, I said it's automatic for them, but it doesn't really have to be. They all know how it works, and he doesn't. They probably have a different method of releasing since their suit is unlocked and they know the system, whilst the red valve next to their head is probably an extra safety measure. He uses it over and over again because it seems to work, whilst it is possible the normal release on his suit doesn't.
Other mistake: When Rita hits Cage's leg with the transponder (that needle machine) during the chase in the garage and time gets slower we can see she is turning the steering wheel to the right, but the wheels are still turned to the left.
Other mistake: When Cage bursts through the roof of the car and shoots the mimic in the caravan look at his armour and weapons - he is now too big to get back into the car - he should be wedged in the roof.