Visible crew/equipment: When Kel gets up to get more water you can see one of the cameras.
Continuity mistake: Ray places a donut that Debra throws at him on the third step and then stands up. Later the donut appears on the second step when Frank comes down the stairs. (00:19:15 - 00:20:45)
Not in the Line of Fire - S3-E15
Continuity mistake: When the vendor throws the hotdog at the press conference, a lot of the toppings/condiments trail behind it. When the shot changes and the hotdog hits Mike, there are no condiments trailing behind it. (00:19:10)
Tutoring Torvald / Gerald Comes Over - S1-E13
Continuity mistake: Arnold switches from his left hand to his right hand when taking the test.
Suggested correction: I don't believe it is ever established whether Arnold is left or right-handed in the series. Without confirmation; he may very well be part of the ambidextrous population that uses both. I used to write with both hands myself in school.
I do believe he is ambidextrous. In "The longest Monday" he is using chop sticks with his right hand. Many other episodes he uses his left hand to write.
Except the mistake is saying he switches hands in between shots during the test. Not that one episode he's left handed and the next he's right handed. Yes, the teacher was shown for about 1-2 seconds before the switch happened. But these mistakes should be considered valid as an actual mistake in animation rather than to suggest to the audience that for no reason whatsoever, Arnold switches hands to finish the test, and only does so when not seen.
I'm ambidextrous myself, and I often switched hands when taking tests. It was very useful for preventing hand cramps. It only takes a couple of seconds to switch the pencil to the other hand, so I don't see why Arnold can't do it within that span of time too.
What Does Blue Want to Make? - S1-E15
Visible crew/equipment: A boom mic is visible when Steve starts singing "We Just Got A Letter."
Continuity mistake: The bottle of orange soda on the breakfast tray Dick tries to bring to Mary changes to a bottle of alcohol (Jack Daniel's I believe) when he sets it down. It later changes back into the bottle of orange soda.
Midori no chikyû wa makasetoke - S1-E2
Other mistake: When Yurika restarts the Nadesico, one of the screens pop up with a huge congratulatory "SAFATY ROCK OFF." (00:18:05)
First Kiss - S1-E17
Visible crew/equipment: At the end of the episode when Harvey hops away, a boom mic is visible. (00:21:55)