I've run numerous games on the MiST A8 core and haven't seen any problems. I've also used Altirra quite a bit and haven't noticed anything particularly "off" about the graphics, sound or scrolling on MiST. In fact, I remember commenting to a buddy that I thought the horizontal scrolling text in Jumpman's title screen looked much smoother than (non-Altirra) emulators that I had used. That's not to say that anyone else's observations are invalid - it could be one of those things that once you "see" it you can't "unsee" it or there might be issues with specific titles that I haven't tried. I can only say I haven't noticed any anomalies during my admittedly casual usage playing popular game titles.
In my opinion, here are some pros and cons:
1. Much smaller than a PC (unless you're comparing to an Intel NUC or equivalent which may end up costing significanty more than a MiST).
2. Instant on - it feels like you're turning on an Atari rather than booting a PC.
3. Completely silent.
4. Two built-in joystick ports that you can plug real joysticks into without needing an adapter.
5. Built-in support for the TurboFreezer so you can do save/restore state.
6. It's a more modern device so (hopefully) less likely to fail than original Atari hardware.
1. VGA output only.
2. No ATX support so it can only run unprotected or cracked disk images.
3. Doesn't support all types of cartridges (e.g. Bounty Bob Strikes Back).
4. No cassette image support.
5. As someone else mentioned, it doesn't have all the bells and whistles of Altirra. Think of the MiST as stock Atari hardware with 4 built-in disk drives and an optional memory upgrade.
6. It's not a mass-market device so if it does have problems your options are limited.
This is not A8 core specific, but I'll also point out that while there are a good number of cores available for MiST, it's much more limited than a PC which can run any number of emulators. If a MiST core doesn't support something you want, you're probably out of luck as opposed to searching for a different PC emulator that may support it. For example, the MiST's sole Apple II core only supports the II+ so it can't run several titles that I'd really like to play.
For what it's worth, I have access to all 3 options: a real Atari, a Windows PC and a MiST. The MiST is what I leave hooked up in my basement to a small LCD TV when I want to play an Atari 8-bit or 2600 title because it's so small and unobtrusive.