Other mistake: When Dick is trying to get into the jewelry store, the clerk keeps trying to buzz him in. When that doesn't work because Dick doesn't understand to wait for the buzzer to finish before he tries opening the door, the clerk goes over to the door and unlocks the deadbolt and opens the door for him. If the door was locked by a deadbolt, then a buzzer wouldn't really do anything to unlock the door. (00:14:05 - 00:15:00)
Revealing mistake: In the scene with www.planetsolomon.com, you can see that it is a pre-filmed video (not a live stream as he said), as it has a time slider and play/pause controls etc. (00:13:05 - 00:13:45)
Other mistake: When Dick is up in the tree fort, the aliens are looking at him through their hand binoculars, but the image is taken from the same height as Dick. However, since he is higher than they are, they would be seeing him at an angle. The view as seen would be impossible unless they were at the same height as he was.
Other mistake: While talking to his therapist, Dick tells her that one of the mishaps that he caused in his relationship with Mary was showing up to a fundraiser naked. While true, this doesn't happen until Episode 13 (Rutherford Beauty) - two episodes later. This was due to the fact that most of Season 5 was aired out of production order.