First, the manner in which second season canon was handled. Second, the movie has quite a bit of ship tease which occurs in the movie which many fans wished would not occur. Third, a new character was added to the team. Forth, there are a ton of unanswered questions. Fifth, the art style is something which has bothered since the posters were released.
I'll address the way the canon for the second season was handled. On the positive sides the makers of the movie didn't forget that the canon existed. The two younger digidestioned still have their upgraded digivices, and the uniforms that the older kids wore for season two are now being worn by the younger two. Matt's band is mentioned, and so is the fact Joe goes to a different school. The only other reference to season two material is a flashback sequence showing the main digidestioned introduced in season two being nixed. There is no telling what else will be nixed in the next movies either. For example, while season two left the impression that Matt and Sora are dating, they aren't in the movie.
A few people will argue that season two's canon trumps that of the movies, particularly when the director and the producer publicly claimed that the material in season two was canon, and some fans even credit the director and producer as the creators of the Digimon series. In reality the series started off as a series of games, and were created by a different person entirely. One of the rumors floating around at the time was that the production team split because of a major rift, and the production team for Tamers was created because of said rift. The movies may thus be seen as a way to fix the issues that occurred later on in the second season, particularly if season two didn't fit what the original creator wanted for the series.
This leads me into the second issues. The movie does not at all shy away from ship teasing. The pairing between Matt/Yamatto and Sora is no longer an official canon pairing, and the love triangle for Sora between Matt/Yamatto and Tai/Taicho is back. Contrary to what the director said, the love triangle did exist within the games of the franchise, and Sora did show an interest in Tai/Taichi. Add to this there is ship tease for a relationship between Kari/Hikari and T.K./Takeru, but this remains under the surface. The most evident ship tease though is between Izzy/Koushio and Mimi. Those rooting for Joe/Jo and Mimi together are out of luck.
Chances are there is going to be more ship tease in the later movies, something many fans were hoping could be avoided because a.) the series is meant for kids, and b.) the series fits into the shounen demographic. The first problem with this though is the fact Digimon Tri is not aimed at kids, but is instead aimed at older fans of the franchise, and as such romance will be a thing. However, in that same turn kids series aren't free from romance contrary to the popular belief. Second, the shounen demographic isn't free of romance either. That's another misunderstanding. The main problem though is people may not be pleased with the pairing choices put down by the movie.
The third issue is the new character. Meiko ends up replacing the four charters from season two, which is something that will not sit well for certain fans. She's not though a bad character at this point. Unlike the characters from season two, her introduction was a lot slower, and she didn't usurp the role of the original eight like Davis/Daisuke and company did. One downside is she may be thrown in there to solve the love triangle issue involving Sora between Matt/Yamatto and Tai/Taichi, which again will be something that may not sit well with fans. She's a lot more soft spoken then Sora, so she pretty much invokes the role of a proper Japanese lady far better. Add to this she's got a major shrine maiden vibe going on, which in turn means she could, if not handled well, turn into a Mary Sue.
Still, this is actually the part I found myself most worried about in the series, as I feared she would usurp the canon characters like Davis/Daisuke and company did, if not worse. She's in reality a very non intrusive character, whose presence did not over shadow the original eight at all, and instead she's slowly introduced as an additional cast member, much in the same way Kari/Hikari was in season one. Her personality ended up being enjoyable, and pleasant. Any character hate at this point is unwarranted.
The forth issue is that there are a ton of unanswered questions. One of these questions is what happened to the four who were nixed, but other questions pop up. Since this is an ongoing series, we'll hopefully see these questions answered. The fifth is the art work. The art work actually isn't bad, but is something that people will need to get used to. One disadvantage is the characters don't look quite the same as they used to, as the art format used for bandai's shows aimed at children are gone, but on the positive side this allows for a whole lot more detail in the art work that wouldn't be possible had they gone with the old style.
As for the plot of the story, one of the reasons they likely released as a movie instead of in episode format comes down to the fact the series plot wise works more like the movies did. While all of the Digimon telivision series are action packed, this one holds back on the action in the same way the movies do. For some people this may be a disappointment, but in the same regard a lot of built up occurred within the series allowing for a nice introduction for the new character. The characters are also in character, or at least for the season one material, and some of season two.
