Yeah, i'm a victim of the system today :P . So yeah - i think some changes should be made. First of all i had verified account via phone. And even then i didn't have any notification that i was banned. That's the first issue for me. It would be nice, if i put such a , for some people private info on the site, to have some profit from it, in such a situations. Even with back up "Hey, you were banned, contact us via e-mail, to solve it" auto reply. Or have even some message, when you try to log in, like anything will be fine.
Second of all - imo yes, it should be hand checked via people . Because machine is "stupid" and can ban you for something which shouldn't be banned. And in both cases - if someone is down voting/reporting comments or if system catch something sneaky. Or any other, when people, just for being petty, or not agreeing with you, can jump on your comment and down vote it, just because. If machine, can't catch some niuances, and you can't teach it, verification should be done manually by human. I'm aware it takes some time, effort and humans to do so, but imo it's worth it. People maybe will think twice, before they will wrote something, report something or vote. And we avoid accidental bans, for words or links, catched via auto.
Third - imo people should know, how the system works, and what can ban them - what type of content, what they shouldn't put in the comments, and i'm aware we have overall some net etiquette, and common sens in the rules. Still, it's grey area for many. Should we not put some content, links, words, anything? because if bot can catch it, via auto and accident, imo people should be aware, what is "dangerous" for them, to put there. Does we have some ratio or other stuff, we should know? Simple, if we can't teach system, maybe teaching members of the site, how to navigate through the comments section to avoid accidentally blocking, might help both sides? Also, imo it would be amazing tip for moderators, to navigate and help better in some situations, especially those in the grey area, to decide what is still fine, and what should be removed.
Fourth - connected to first imo we should have some clear info, that we were banned. Because i was really confused at first.
Fifth - as @Kate mention, some list and more mods. So everybody will have clear info, when, why to who, they should respond or send their issues. And maybe overall some "emergency" contact, when i can't log, and for example staff page also doesn't work, so i would know, what to do step by step, when i have some issues, and it's ASAP stuff.
Probably i should write more but i forgot. Anyway the point is - more clear rules, what can be banned (transparency not only with overall content but also some technical issues, like ratios , forbidden links, spams etc. ); better system to inform member, that she/he was banned and what to do after that (who should be contacted, maybe the reason etc.) ; clear list of people, who should i ask, or seek help, in any comments section issues ( because as far i know, some of AStaff sometimes also are noted about the issues, and sometimes they can't do much about it); and most important, adding HUMAN factor to the whole banning system, for verification, if "machine" didn't made a mistake, and ban someone innocent.