I haven't had any issues (no pun intended) with it. But then, I also haven't bought a ton of comics through it, either.
Now, it is owned by Amazon and some might see that as kinda problematic in and of itself, but the controversies I can find seem pretty unremarkable. Not that I agree with their choices, but it seems like the kind of stuff one would expect from a major distributor of comics. Controversial bans, conflicting business interests, the usual.
The Android app has a good navigation system and seems pretty user friendly overall, so that's good. I definitely feel like it's the better option when it comes to on-the-go comic viewing.
All that said, it is a digital distribution platform and those have their own, unique potential issues. Like the possibility of a digital book being removed from your device without your consent. Buy a physical book and it's yours, period. Amazon can't retroactively decide you aren't allowed to have it.
But, if you're not to worried about that, then, yeah, Comixology seems like a pretty solid thing.