Other mistake: In the scene immediately after the opening credits, Jim is talking to Melinda on the phone. Right as he's hanging up, someone calls out "Dr. Clancy? Got a minute?", to which Jim waves in acknowledgement and starts up the stairs. (Jim's spirit has been in Sam Lucas' body since season 4 and in an earlier season 5 episode, his white coat is embroidered S. James Lucas, M.D). (00:09:15)
The Southern Air Temple - S1-E3
Other mistake: When the gang is in the Hall of Statues of Past Avatars, Katara points out the avatar cycle pattern of statues and Aang zeroes in on Roku's statue. The earthbender avatar statue next to Roku is of an unknown man with a sword, not Kiyoshi. (00:12:50 - 00:13:35)