Is it at all possible for a permanent porcelain crown to go on the wrong way?

Your crown will only fit correctly one way.  Schedule an appointment with a dentist and have it recemented properly to avoid future problems.

Possible I guess yes, probable no. If the crown is made correctly it can only go on in one way. For it to go on backwards the tooth would either have to be prepared the same on both sides or else the crown will not fit.The real answer is that for the crown to go on backwards would normally mean that it does not fit once cemented or bondedGet it removed and remade.Dr. Cary Ganz