Other mistake: When Harry spits baby food on the baby (the camera lens in actuality) in retaliation for the baby spitting food on him and Tommy, Joseph Gordon-Levitt breaks character and laughs uncontrollably and looks at and gestures to off-screen crew members a couple times. (00:06:25)
Continuity mistake: When Jennifer comes into work the next day after her dinner date with Dick, her face is covered in hives from an allergic reaction. Later when Dick interrupts her choral group, the hives on her face have disappeared. She and Dick are wearing the same clothes in both scenes, so she couldn't have overcome such a reaction in such a short amount of time. (00:12:30 - 00:15:00)
Other mistake: When Dennis Rodman sees Harry, Tommy, and Sally at the hardware store, he addresses all three by name and asks what they are doing on Earth. If he didn't previously know they were on Earth, then he couldn't have known they were going by those names, as they chose those names after arriving at Earth. Harry even mentioned in a later episode that the names Tommy, Dick, and Harry were chosen by chance when they saw the phrase "Every Tom, Dick, and Harry" written down.
Continuity mistake: In 1-2: "Post Nasal Dick", Harry has a dream about Martha Stewart. But in this episode they panic because they dream and have nightmares and don't know what they are. Shouldn't Harry have panicked when he dreamed about Martha Stewart?
Continuity mistake: Dick's plot in this episode is that he learns about the concept of tipping. However, the season 3 episode "Eleven Angry Men and One Dick" showed that Dick was already familiar with the concept of tipping when he tipped a bailiff during a jury selection process.
Character mistake: Sally tells Dick that he's jealous of her gig as a weather girl because he's never been on TV. However, Dick did appear on TV as a panellist on a talk show highlighting Dr. Strudwick's physics book in the season 4 episode Dick vs. Strudwick. Dick ended up turning the show into a Jerry Springer-like fiasco, and Sally even attended the taping. (00:10:40)
Continuity mistake: When Ms. Dubcek is showing the Solomons the attic apartment in the pilot episode, they enter (and she later exits) through what is Dick's bedroom in all subsequent episodes. Additionally the staircase at the back of the living room that serves as an entry point is completely missing.
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)