Yeah noticed that too. The same happened with my female character, but that was already to be expected in the code (though it would be nice to be taken care of as well).
One strange bug i've encountered is that randomly, Chloe will unequip one of her weapons. I didn't use editors or anything, and this situation doesn't seem to have any special reason. I get it, as I said, randomly.
Yes, clicking to bypass the FMV disrupts it. I also experienced something similar, when Chloe asked to go to an Inn (after dealing with her quest), and if I clicked while the FMV played, the dialogue would not come.