The most glaring omission is the built in player has no concept of a music queue. You cannot decide to play a new song while listening; the only way to queue up music is to create a playlist ahead of time.
You can't install new apps via the Play Store from what I can tell. By default it whitelists what can be installed over a usb cable. Luckily you can remove the whitelist and install any apk you want by clicking on a particular page in the settings 6 times (iirfc). I ended up installing Poweramp this way and it turned my opinion of the purchase from a massive disappointment into a mild one.
Other complaints are that they advertise Airplay compatibility but it turns out it's for receiving only, not sending. So you can send music from your iPhone to the FiiO and have it send it out from there using the FiiO's DAC. I was hoping to actually use Airplay to send to my home receiver from the FiiO, but that isn't possible. I use Bluetooth instead, but the range isn't great and when I scroll through my library while music plays I get skipping (possibly because the Poweramp app is hogging cpu, but again, the built in app for playing music is a non-starter for me).
I would really love for there to be a dedicated music player that went above and beyond in terms of user experience as well as audio quality, but for me the FiiO M6 at least isn't it.