Revealing mistakes: For the famous "mirror reflections" in which Sam sees who he leaps into, the series used the old trick of a dual set with a clear glass in the "mirror". Scott Bakula would stand on one side and the actor playing the person he leaped into on the other. If you look really close at the glass, you can see sometimes Scott Bakula's reflection. (Especially if the mirror is near a source of light like sunshine).
Continuity: The episode "What Price Gloria?", the first episode Sam leaps into a woman, suggests that Al sees Sam as the person Sam has leaped into since he is checking him out. However, later in the series, in the episode "The Wrong Stuff" he leaps into a chimp. It's obvious that Al can see Sam as Sam since Al can understand what he's saying.
Continuity: In the first few episodes of the series, Ziggy is referred to by both Sam and Al as "he". Throughout the rest of the series, Ziggy becomes a "she".