Comfort level with the person we are doing work for.
*Unreasonable expectations Scott is right, you can't clean a 5-bedroom smoke damaged home in a day. If they think you can and expect it to be done for a couple of dollars, you've got problems.
Can I trust them?
Can you work for them and trust that they will honest with you and the insurance company. or Are they just looking to get something out of the loss.
Will they pay me?
The most dangerous comment is "No I don't need an estimate, it needs to be done" That's a trap, usually once completed they are the ones to complain about the price.
Are they mentally stable?
Can I work for them and we complete the job without them having a melt down. Are they going to toss me off the job and try to sue me?