Winning Through Intimidation - S1-E15
Continuity mistake: Panik's Metal Guardian can be seen on the field several minutes before he actually plays it. (00:10:30 - 00:13:00)
Duel Identity, Part II - S1-E30
Continuity mistake: Yugi mistakenly says if he doesn't get a monster out to defend himself Mai can attack him directly, which wouldn't be possible since the rules of Duel Monsters during the Duelist Kingdom arc forbade direct attacks on defenseless opponents. That rule wouldn't be implemented until the Battle City arc.
Champion vs. Creator, Part II - S1-E27
Character mistake: Pegasus says his toon world cannot be penetrated, but that is not true since it's a magic card, so any card that destroys magic cards can destroy it. Furthermore, monster special effects can also destroy it.
Winning Through Intimidation - S1-E15
Deliberate mistake: In the actual card game, attacking the castle ring would not be allowed, but this is probably done in order to enhance the show for kids.