My main concern would be if something turned up missing at a job; the ex-offender would be the lead suspect just because he's there.
Never mind that someone else is the culprit; people unfortunately jump to the easiest (usually wrong) conclusion. In fact, I know some people who have REFUSED to accept a set of master keys just because if there's something missing, they can't have the finger pointed in their direction.
He could be the most trustworthy guy on the face of the Earth, but an absentminded customer could easily misplace their wallet and start crying that "it must have been stolen".
Most of these guys have paid their debt and deserve a fresh start; the few who will be trouble will usually show themselves early enough that you can either not hire them or put them on a job where you can keep an eye on them.
