From what I can tell, if I want to see if someone replied to a comment I wrote, I have to go to my profile and look up "search for myself in comments." Or, say, if I was getting into a heated argument or doing minor rule violations I wouldn't even be aware I was getting warnings to cut it out until I suddenly couldn't log into my account anymore or went to my profile and saw I had a record.
There doesn't seem to be a notification icon with a number attached to it to get your attention like on Derpibooru or Deviantart, which in the latter case would be a problem since if someone was new to the site they could get banned without even being aware they were breaking site rules. I am aware it would be partially on them for not reading the rules, but it also feels important to have a way to be made aware you've broken the rules before a banhammer comes down.