Factual error: When Homer leaves the orphanage the trees along the drive are in their October colours - yet just a bit farther on, the trees that should have autumn colours, are fully green. The first Fall Homer is away the season seems to go on and on with very little sign of leaf turning. It's also highly unlikely that anyone would be driving around much at night in a convertible at that time of year in Maine. It would be extremely uncomfortable.
Revealing mistake: When Homer is sitting outside (on a dock?) reading a letter from Dr. Larch you can see through the envelope and the letter because the white paper is thin. You can tell there are writings on the letter but it is equally obvious that the envelope is blank with no address written on it.