"Check Transmission" and "O/D OFF" lights started flashing on my 2002 Ford Explorer the other day...?

No fault of the dealer due to the hinge replacement, don't even have to raise the vehicle to replace the recalled rear gl hinges. It may be input or output speed sensors on the transmission causing the blinking light, that is the usual cause on the Explorer for the flashing OD light. Nothing the dealer repaired on the back gl would have caused the light, just a coincidence. A roadtest with the diagnostic tool attached will tell which trans speed sensor is not reading.