Deliberate mistake: The show is set in New York. Joey was a cast member on Days of Our Lives, which is filmed in Los Angeles, but is still always around.
Deliberate mistake: When Johnny is watching the news footage of the Hulk battling Thing, all the footage is merely clips from that portion of the episode, including parts of the battle that were happening before the camera crews even showed up. (00:02:50 - 00:07:20)
Deliberate mistake: Though he moved freely about the station in his environmental suit, Kosh was never actually seen going through a door. He approached doors, but then, sometimes rather disconcertingly, would suddenly be shown on the other side. The reason: look closely and you'll realise his costume was too large to fit through any of the doorways on the set, so in reality the character would never have been able to move around the station.
Deliberate mistake: The show regularly shows characters by the Chicago River and either on or near Michigan Avenue, when they are getting lunch or walking to work. Both U of C hospital (where the hospital exteriors are filmed) and Cook Country hospital (where the characters are supposed to work) are about 5 miles from this point. This would be an extremely long distance for them to walk on a routine basis. I'm sure this is done just because Michigan Ave and the river are two of the most scenic parts of Chicago.
Deliberate mistake: When the sewer worker is trying to escape the Lizard, the fast lanes in both directions of traffic are visibly clear for several blocks, which is extremely unlikely in downtown New York. (00:01:10)
The Defection of Hawkeye - S1-E8
Deliberate mistake: When Mandarin is watching and wondering why Julia is tailing Clint, the road surface and cliff walls around Julia's car are recycled repeatedly. (00:10:55)