On at least one occasion, a Starman was red instead of the proper yellow.
In the Robo-Koopa episode. as appears on the 'Mario's Greatest Movie Moments' DVD, the DVD subtitles misspell "Koopa" as "Kooboo" near the beginning of the episode.
The animators forgot to draw a face on the character of Indiana Joe. That is because in the "Indiana Jones" movies, Harrison Ford's face (especially in the beginning of Raiders of the Lost Ark) is sometimes covered up by his hat.
In early episodes, Toad's hat is the wrong color (red with white dots, as opposed to the proper white with red dots.)
In some episodes, Mario and Luigi gain the ability to throw fireballs from a Starman. While Starmen make a character invincible, they don't give them the ability to throw fire (Fire Flowers do that).
In the opening credits when Mario and Luigi run across the screen, Luigi noticeably slows down as he reaches his "mark" at the end.
In some episodes, one character's mouth will move but a different voice over is heard and say something different.