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.
Continuity mistake: As Harry is leaving the party he is dry despite having just been in the shower fully clothed.
Continuity mistake: In the scene where Harry and Tommy are sitting in the living room, Sally comes by with a drink for Tommy and the shot changes when she is behind Harry and walking towards Tommy. But in that next shot, Tommy is already holding the drink.
Revealing mistake: Harry put his feet in a pot of warm chicken soup, yet at the end of that scene when they hug each other Harry lifts his feet up and you can see his socks are dry.
Visible crew/equipment: When Dick wants to go along with Mary to a wedding he tries to convince her. When he says "Whatever it takes, I'll do it" he walks forward. Take a look at the top of the screen and you'll notice the shadow of the boom mic on the wall following him.
Continuity mistake: When Nina asks when Dick's birthday, is the papers on the back of her clipboard change position between shots.
Dick Is From Mars, Sally Is From Venus - S1-E4
Continuity mistake: In this episode Dick decides that Tommy has to go to school, but in 1-2 "Post Nasal Dick" Tommy already goes to school.
Suggested correction: That's just because these episodes were aired out of order of their production. "Dick Is From Mars, Sally Is From Venus" was the 2nd episode produced (production code 102) while "Post Nasal Dick" was the 5th episode produced (production code 105).
Continuity mistake: The dog that Harry brings home suddenly has a collar after Dick sets him down on the table. (00:02:40)
Continuity mistake: Mrs. Dubcek says that she doesn't allow dogs because she is allergic to dogs, but in a later episode she claims that she doesn't allow dogs because she has 6 cats buried in the back yard.
Continuity mistake: When the dog is on the table, the book on the right of the table changes position between shots without anyone touching it.
Other mistake: Sally mentions that she makes jello with cheese, but many times the aliens have shown that they are terrified of Jello.
See Dick Continue to Run (2) - S2-E1
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.
Hotel Dick - S2-E3
Revealing mistake: Right at the beginning of the episode as the camera pans over to the doors of the movie theater you can see the actors playing the Solomons waiting for their cue to come bursting out of the doors as if they were running out of the theater.
Continuity mistake: In the beginning when Dick is talking to Sally and Harry about Mary, the position of his tie changes after he says "what's the point."
Continuity mistake: When Dick gets out of the chair to talk to Tommy, his newspaper is on the chair cushion. Later, it's on top of the pillow.
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 the baby Is in the ball pit you can see that he is at the edge. When they show him again he is in the middle, the last time they show him he is at the edge again.
Proud Dick - S2-E13
Revealing mistake: When Harry lands in the yard, you can tell he lands on a crash mat, as the grass beneath him shuffles. (00:01:15)
Proud Dick - S2-E13
Other mistake: When Dick and Sally are playing with the cat toy in the kitchen, they make a lot of joyous noise while doing so. When the shot changes, we see Mary coming up the stairs to a completely silent home, and she can't seem to locate anyone until Harry pulls her into the closet. The kitchen is only a few feet away from the stairway, so not only should Dick and Sally's voices have still been very audible, but at the very least, Sally should have been in Mary's direct line of sight. (00:15:53 - 00:16:20)
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.
Suggested correction: What the camera shows is for the audience. It's not meant to be a POV shot of what the three are seeing.