I can't give you any specific examples, but as a Firefox user, I can tell you that many forms, especially e-commerce checkouts forms, are slightly broken in Firefox. They are often broken enough that you must switch to Chrome to submit a payment.
This really surprises me. I've used Firefox exclusively for years and have never not been able to complete an action because of it (unless it was my own fault - disabling required third party scripts, etc). Why can't you give examples - is it just memory, or something else?
It's never bigger places like Amazon, I've only had it happen on little shops like websites that sell Indie games. I don't remember which ones it's happened on, but it's happened a few times. I shouldn't have said "many," it's just that it's quite irritating when it happens.