I just noticed this demo! I've been trying to keep up with this game since I first fell in love with it after seeing it on Super Best Friends Play, but I guess this just slipped through the cracks.
I ran into a glitch during what looked like the final boss, in which all of the turn bars- including the boss'- stopped filling.
Everything else seemed to be fine for the most part: the idle animations still worked, the "conveyor belt" kept moving, I could still pick things up, cook, fill my cooler (cool addition, by the way) with said food, reload weapons, and even use items like the repair kit. Anything that involved the movement or combining of items seemed to work as usual.
What I *couldn't* do was attack or eat with Cassie, use support items with Jack, or be attacked by the Bacques Dau.