Continuity: Tai says "And it started to snow in the middle of July" but later you find out that it takes place on August first.

Other: Series 1, Ep 15, The Dark Network of Etemon: Watch the scene where Biyomon and Palmon are eating. A Pagumon passes, Biyomon turns her head and then has two beaks. Obviously a frame overlap.

Plot hole: Series 2: In the episode where Yolei and Sora go to Russia, they can't talk to the Russian kids, because they can't speak Russian. However, the Russian digimons speak English and they surely speak Russian, so Yolei could just have asked them to translate what she was saying.