Alternate Character Interpretation: The characters' depictions have generated some issues with the fans; Marisa is more of a Straight Man type, Sakuya is more kindly and gentle than her expected "Perfect and ElegantMaid" persona, and Reimu is a bit of a Jerkass at some points ("Patchouli, get up, we're in the middle of a conversation here!") Since the production is only beginning, however, these remain to be seen.
Must be noted that alternate interpretations abound in Fanon and the abovementioned (with the exception of Marisa) are actually a bit more common than most.
Broken Base: Fans have been divided over whether or not the anime is a perfectly acceptable piece of fanwork, or if it's a complete slap in the face to ZUN's desire to keep the games from being overshadowed.
Internet Backdraft: ZUN's demand for a title change and his accompanying explanation earned lots of flak (at least on Sankaku Complex); things like "He's just butthurt over the fact that the fanworks have become way more relevant than the original games".
Aoi Yuki as Youmu could count: Taking into account she previously voiced Madoka Kaname, one could take as granted Youmu would sound like Madoka. She sounds more like a tomboy instead, compared with her master Yuyuko.