In recent history, an 'evacuation trainer' caught fire in 2016
To my knowledge, the only fatal accident in a simulator involved a non-simulated plane actually crashing into the training center building.
In my experience wrist injuries, broken arms, etc. on FFSs can sometime happen, especially if the instructor does not wear the seat belt - 'glitches' in the visual database while taxying on the ground can sometime result in sudden accelerations.