So far there are no major problems. Disk was filling up but probably unrelated. I guess beehaw grew a lot more in terms of percentage than lemmy.ml during this time.
The main things I can think of which might help are to increase database pool size (in config file) and number of federation workers (/admin). Also create a swapfile if you are running low on RAM.
I mean I've been able to verify with a number of users in America, and in Europe that signups just "spin" on lemmy.ml and have been that way for 24 hours or so. I've personally tested it on iOS & Windows (Safari, librewolf and Vivaldi) as well as on multiple IPs and had a few friends in multiple countries (England, France and Germany) try as well. Something is hung up somewhere for a few people at least. I made a post about it shrug
Also there's a few posts on r/lemmy with others having this same problem too.
You can ask them to check the browser console for errors. Or sign up somewhere else. Anyway we are getting at least a dozen signups per hour so it's working for many.