Continuity mistake: Russell first slept with Constance on his 18th birthday. He says she was 39 years old at the time. She is now 60, so 21 years have passed, making Russell himself 39 now. However, in the Season Two episode "Time Share", he admits to a magazine reporter that he is 42 years old. There is no indication that three more years have passed.
Bag Ladies - S2-E5
Other mistake: In the first scene with Russell and Claire, Claire is portrayed as being too young to understand his references to Ross and Rachel from "Friends", Ward and June Cleaver, or the song "9 to 5." Later, he tells Adam that he met her while she was playing Grateful Dead songs in the park. That alone would demonstrate that she can be aware of shows and music from previous decades. On a side note, "Friends" ended only three years before this show began.
Russell's Father's Son - S2-E13
Visible crew/equipment: In the bathroom scene with Audrey and Jeff, you can see down the hallway and there are visible people in the background standing in their living room.
Continuity mistake: Jeff and Adam meet at their favorite diner for supper. The scene opens first with a street view of the diner, and it is obviously night time. Inside the diner, when the camera is on Jeff, sitting in his usual booth with his back to the entrance, we see the the cash register over Jeff's shoulder, and in the front window behind the register we see that it is broad daylight outside. Every time the camera is on Jeff we see through the front window of the diner that is daytime outside, not night.
Continuity mistake: Timmy agrees to marry Russell because Timmy's work visa has expired and he will have to leave the country. However, in the season 5 episode "Double Down" Timmy states that he has been a US citizen for many years.
