Hello - I'm a computer scientist and developer for many years now and I know, that bug-free software does not exist beyond anything trivial.
So, I feel, that the switch to the new site was a little bit rushed and testing clearly did not catch many pretty obvious bugs, IMHO. Still, I voted to keep the new site and not to switch back.
Since writing good test cases and reaching full or at least sufficient coverage of all use-cases is incredibly hard and time consuming. The best thing, you can do now, is to find and fix on the actually used system (please have a staging server for changes and fixes!).
I think, your user-base detects a lot of bugs here and I think, a very useful thing would be to have a very simple and quick to find thread or web-form where to report bugs and and/or usability-issues. The relates thread could also contain a list of already reported issues and info, if the issue is accepted and if so, which priority it has to be fixed (and maybe let users up/downvote issues). This way, you get the most valuable data, what is desired by the users and what annoys them the most - weighted against the effort to implement/fix it.
Helping us helping you would probably the fastest way to quickly improve everything until we all feel back at home with the new site.
In any case, all the effort is highly appreciated and admitting, that things didn't go as well as planned shows some courage. Don't see that often in software-world.