The first one I encountered i'm gonna nickname the "Infinite Call", inwhich the call you're on never seems to stop.
I accepted a call of a pursit of an armed suspect. Went to the place, (behind Fleeca Bank on Chumash, if that helps) ran in and died instantly. I respawned and used the "GotoPD" command in RAGE, and all of the police there were in a "I'm gonna shoot something" stance, and the red dot of the suspect was still on my minimap. I could still arrest people and perform traffic stops, although I wasn't getting anymore calls. I'm sure you could still go to the pursit and finish the call, but that's kinda annoying. I fixed the bug by going off, then back on duty.
The second one i'm gonna nickname "Arrest Softlock", inwhich you become frozen, and can't move while arresting someone.
I accepted a call of a Grand Theft Auto, made the suspect(s) crash, and was able to cuff one. I went to cuff the other, but the other 20 or so police began to shoot him while I was in the process of arresting him. He died while I was getting him up, and I froze. All form of movement was locked. I fixed the bug by putting in the "GotoPD" command in RAGE.