It's funny the OP mentions this 'continuity error' when there a more blatant error in TSFS..
When David first opens the lid the shot reveals the interior to be dirty, but then a few seconds later another shot shows the interior to be be perfectly clean. That one can't be explained and is much more annoying.
It might be vice versa--first clean, then dirty, but it's a terrible error.
I still want to know where all that extra damage on the Enterprise comes from between TWOK and TSFS
LOL. True, but at least time passed between end of TWOK and TSFS.