I think there are now three threads on this now . . I know from experience, it's not the easiest problem to fix!. You can still access everything by clicking on the top left hand corner, "Try live version".
Unfortunately these things happen with websites, it's no-one's fault and really tricky to fix. I used to administer our school website and this kind of thing drove me mad, everyone wanted an instant solution.
This BAD GATEWAY is a nuisance. I've been getting it all morning. I gave up trying to join the chat for quite some time. It's not the first time it's happened, but today is worse than before.