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.
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.
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.
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.
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)
Answer: Digimon started as a series of virtual pets, making them digital. In the television series, Digimon live in the "digital world."
Bishop73