At 1:18:05, after leaving warp speed and being fired upon by the big ship, you can first see the big ship closest to the Enterprise and then the moon in the middle and the earth in the background. The moon is 384,400 km from earth and they said it was 237,000 km from earth, so that is the first mistake in the scene. Also the earth would be smaller than shown in this shot.
At 1:24:51 the Enterprise is beginning to be aligned to the undamaged larger ship which should be stationary because there is no reason to suggest otherwise. At 1:39:40 is the last time you see the moon, and it is still close with the large ship in between.
At 1:40:14 the Enterprise central power grid fails, but, being so far from earth, the gravitational pull is not strong enough to pull an object that hard, especially that far from earth seeing as gravity gets stronger the closer your are. If it was, we wouldn't have any (artificial) satellites.
7 minutes later the Enterprise reaches the tops of clouds at 1:47:15. Instead of the distance from the moon, let's use the movie figure of 237,000 km from earth in 7 minutes that's 2,031,428 km/h or 1,262,270 mph. For the movie sake, let's say the ship's outer hull can withstand the temperature and other forces of stress at that speed, the ship was damaged and the inside was exposed, it should have been ripped part.
As for the crew members falling in all directions I found this to be another mistake. It started in microgravity so the effects should be minimal. It should have been the ship pushing around the crew. In microgravity the ship should have moved first and only pushed crew members after the object in motion (Enterprise) set other objects in motion (crew).
With all that off my chest I feel better, and I still would recommend this cool movie to others.