The warning was there in the preview, I just missed it 



[b]Looks [i]like BBcodes still don't like tags being mixed together.[/b][/i]To be fair, most people are going to use Ctrl+B/I/etc. to add the tags, (or the buttons) which will obviously never have that error. Besides, although it'd be nice for it to work regardless of the configuration, it really isn't necessary, nor is it too much to ask IMO for users to just fix their BBCode in such a case. EDIT: added [noparse] so the quote would work.
On mobile, I have to select the reply button twice. The first time causes the ratings to appear, and the second time actually selects the reply button.I'm on mobile right now, and this isn't happening for me. If I tap the quote button the quote is made after a second, simultaneous to the ratings popping up.
Perhaps custom tags would be ideal.But that would require moderation, and would make filtering impossible. It's easier to have a broad list of tags, fit for most (if not all) circumstances while keeping the list manageable.
A limitation of "x posts to graduate" is that someone could spam out posts and graduate, in which case they'll have privileges until they are caught out, at which point it may be too late. Of course, I'm sure you have already considered that. How about a minimum time AND post requirement (not just OR)? This means participating members of the community who have been around some time would be promoted. Of course, you'd include your more sophisticated factors too.Or only allow 'New Members' to post once per x minutes, and if they keep posting exactly x minutes after the last it's very likely they are a spammer trying to game the system, and it can be detected and handled appropriately. EDIT: Or maybe require that everyone does a captcha before being graduated into the next tier, or at least for the first graduation. That would filter out all the bots, at least.