The tumbling scene stars just after Sulu says they've been caught in Earth's gravity and are being pulled in. Then Spock states that gravity is failing. The external shots show the ship tumbling and crashing towards and into Earth. Nothing stuck out to me about it.
This scene deserves little defence.
The main reason it annoys me is because it was trivial to fix it. It would have been enough if that line said "Artificial gravity is failing. Gravity generators are going crazy" There, a tiny addition, and there's no longer a problem with it. The implication that they were somehow pulled by Earth's gravity took me out my suspension of disbelief and I couldn't enjoy the scene as much as I would have otherwise. I have watched astronauts on YouTube, and they don't fall towards the Earth (well, literally they do, but you know what I mean).
If the artificial gravity was buckling, the scene would be equally fun, enjoyable, whilst being realistic and not leaving me wondering "What? Why there are falling?" It is also a decent way to acknowledge the existence of artificial gravity, to familiarize the audience with it without the use of boring lengthy technobabble that ruined a lot of the old Trek (and was also quite often incorrect). It's just sloppy not to write it that way. I am sure they could have found a couple of thousand dollars in their 190 million dollar budget to weed out simple inaccuracies like this.
Contrast this with the weird black hole physics shown in STXI (another thing that I enjoy to complain about cause it makes little sense). They don't really bother me that much, because if you
had realistic physics there, you'd totally ruin a few exciting scenes, not to mention the entire premise of the film. And the weird physics are easily explained if you imply that red matter breaks the conservation of energy, creating new mass for the black hole. Since it is from the future, the crew is unfamiliar with how it works, so it is also natural that there is no explanation in the dialogue, blah blah blah.
OTOH, this here has little excuse for being the way it is, and it is somewhat of a major hiccup. But whatever, I still explain it away with crewmen speaking off the cuff instead of the real reason. It is nowhere near as bad as the lack of acknowledgement of the thousands of dead in San Francisco, but it is certainly worse than than any inconsistencies in the starship proportions, size, or compartment placement (i.e. this entire thread and the aft nacelle one).