A ton. Mozilla is already behind on all kinds of miscellaneous less used standards implementations compared to Chrome AFAIK. On top of that there are security fixes needed monthly and realistically you need to be able to push emergency patches within 48 hours or less (really 1/4 or 1/2 that) or people are going to flee because they got cryptolockered because of you.

How quickly would sites be unsupported? Hard to say. Most likely large chunks of the internet would start blocking Mozilla user agents as an out of date security threat for their userbase before it actually ran into actual implementation problems. The problem would be that, websites and services no longer even bothering to try to support Mozilla and making changes that break things, and of course security holes and exploits which would likely eventually lead to no-click complete computer compromises and other very bad things. Once it falls far enough behind on standards a lot of sites will block it for that reason because they don't want bug reports or to spend money chasing down an issue potentially caused by an out of date piece of software.

Google or whoever owns Chrome would keep pushing new web standards at a fast pace to kill and bury any attempts to keep Firefox running. At that point there's nothing really stopping them closed sourcing large parts of Chrome to kill privacy forks and lock down control of the web which most big websites would be fine with as Google's interest is in getting through ads and preventing the end user from control over their own computer in favor of the interests of the website owner.

It would be apocalyptic potentially for what remains of the open web and user freedom.