This isn't a major problem, but I've had this since version 0.91 so I figured I'd go ahead and post something.
It doesn't happen often, but sometimes when I'm going through the different police vehicles at the vehicle selection the model won't load. My guy will just stand there, no car, and nothing in the game functions (can't walk around, can't force LCPDFR off, ect) other than Esc for the pause/options menu.
I've modified the cars I have available to me, would the "complexity" of the vehicle model have an effect on this? Also, scrolling through them faster seems to increase the chance of it happening.