So far I've seen several things,
in the tutorial levels involving the Borg, one phased through the containment field, and another disappeared when moving into one of the tables in the area where the items have to be destroyed. It phased into the air and practically dropped right on top of my character. Another drone got stuck on one of the tables, and even the animation seemed to freeze.
Just afterward, the first time you get to control a ship, I had the glitch where the character was shown in space instead of the ship occur, as well as I guess losing the first officer you can recruit.
Only other glitch I've had so far is on the Vulcan patrol mission, the area with the seven Orion dry-docks. One of the cruisers phased half through the top of the dry-dock and got stuck in it.
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