Character mistake: Tai says "And it started to snow in the middle of July" but later you find out that it takes place on August first.
Plot hole: When the DigiDestined return to the real world, Izzy states that only a few minutes have passed by despite the weeks that have elapsed in the DigiWorld. However, in an earlier episode, Tai returns to the real world for hours and upon his return to the DigiWorld, only a few weeks have passed by.
The Dark Network of Etemon - S1-E15
Revealing mistake: 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.
The Crest of Sincerity - S1-E17
Continuity mistake: In the scene where the DigiDestined are running towards a cactus mirage, Patamon is visible instead of Tokomon. (00:03:20)
Other mistake: In the English dub of the series, Tai's last name is Kamiya; however, when he makes reference to the family name plate his father put on the front door in this episode, the name displayed is Yagami. (00:03:00)
Character mistake: Agumon says that they were away from the digital world for a couple of days. But in the previous episode Tai and Agumon were back on earth for only a few hours.
Now Apocalymon - Part 1 - S1-E53
Character mistake: Gabumon says that all of the Digimon are at their rookie level, but Gatomon is not a rookie level Digimon, she is a champion level Digimon.
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.
Other mistake: The DigiDestined refer to Arukenimon by name before she formally introduces herself. Before her introduction, it is not established that the strange woman is in fact a Digimon.
Guilmon Comes Alive - Part 1 - S3-E1
Audio problem: When Jeri starts miming with her sock puppet, it is sometimes out of sync with her voice. It is most noticeable in the part where Takato has detention.
The Dark Heart of Friendship - S4-E25
Continuity mistake: Asuramon's faces keep changing positions. One shot his yellow/happiness face is on the left, the next it's on the right, and the same goes for his blue/sadness face.
Answer: We are never told as to how they got there.