Steve, I feel your pain!
I think it has also borked NoScript (if you use that) I keep getting a broken pop-up, warning of a cross-site scripting "funny", on sites (such as this one) where it shouldn't appear. Disabling NoScript, I hope temporarily, seemed to fix quite a lot at the same time. You have to go to tools --> add-ons (I think - writing this on Android!), then disable NoScript.
I use both FF and Chrome (Google) for work, both on Linux desktop(s) and other code-tweaked "proprietary" browsers on Android. Chrome is oftn slightly faster, but it "phones home" a lot about my browsing activity and has an inelegant, crude and unhelpful approach to storing site access credentials. I prefer FF by a long way, although its own new GUI is poor on both desktop and mobile devices.
So do as Mr. Pike advises above: turn off the add-ons, and turn them back on one-at-a-time, to see which one, if any causes things to break.
Awkwardly, you might even find that enabling them in a different order would make a difference, too. So do one at a time and then try the browser for a bit before moving on to the next one (the earlier code needs to actually initialize/run to see if there's a precedence-based issue, so do't turn on two at once). Note that I can't think of a reason why this might happen, but it's not unheard of, and as you know from your background, the number of "states" that are possible (for the software to get itself into) increases exponentially(literally) with the number of possible interactions, so it's quite possible a state on your machine simply wasn't tested. This is very unlikely nowadays though, as testing has become highly automated.
Aside: I really wish developers would realise how badly wrong Apple got the iOs GUI and not keep trying to copy it. There are basic human factors mistakes in it that make it extremely hard for those unfamiliar with it to pick it up, for example not having visual cues clearly distinguishing controls from label text and simple chrome. People (younger ones in particular) learn it, by trial-and-error experimentation, but it is not intuitive. Given how much money Apple puts into "design" they should be thoroughly ashamed of themselves for such a poor outcome, and the fact that both Google and Mozilla* have basically aped them in their own GUIs is very depressing: "Let's do this really stupid thing because our competitors are doing it." I was shocked by my first "smart" phone's poor interface, my inablity to customize it and the dreadful lack of proper documentation, and they have got far worse over recent years - more like jewellry than functional tools.
My 90-year-old mum struggles with a big, clear iPad, simply because its GUI is, frankly, stupid. How she's going to cope with the new Firefox I have no idea, and I'm not at all keen to try to help her with it, because I have no simple explanations for what Mozilla have done, apart from, "Sorry, I know it's dreadful, but...".
But then people buy jeans with deliberately made holes in them and worn fabric. I've got an idea: Let's swap all our vehicle wheels for hexagonal ones because they're new (and therefore much smarter).
E.
(currently in the middle of dumbing-down the content of a company web site so that it "works" on mobile devices, and trying to stop junior staff from "correcting" English syntax because they believe it's wrong).
*I almost wrote Mosaic. That's Freudian, as their GUI/chrome was a great deal more accessible.
