One more possible issue is that some apps may misbehave due to ad blocking. For instance, there was an issue with Play Music, it was repeating ad request hundred times every second. It should be easy to track such misbehaving app in Adguard's "Apps Management" section.
Btw, in the next AG version, we will also add Samsung Knox support. This is some kind of a "legal root", so you'll be able to use proxy mode even on an unrooted phone.
Edit: apparently, Samsung Knox is available on Samsung devices only