Other mistake: In this episode Voyager sends the doctor to a federation ship in the alpha quadrant through a transmission using an alien communication network. Right before he is sent you see him in the astrometrics lab and he steps up on a platform wearing his mobile emitter. His program is then sent through the data stream and the mobile emitter is sent with him. Then when he arrives it is not there. Firstly, the mobile emitter can't be sent this way, only the doctor's program can. It can be beamed but that was not the case here. Secondly, in other episodes where the doctor is taken offline while wearing the emitter they show it drop to the ground. They don't do that here as it appears to dematerialize with him.