Hmmm that's very weird, you're right. No-one has every reported it before.
You need java for this site, otherwise much of it will not work. What I recommend, is un-installing FF (saving your bookmarks, or not removing them as part of the un-install). Then download it again (latest version). Don't put on any add-ons what-so-ever, and monitor it for a while.
Also I wouldn't recommend clearing your cache every time you close the browser. It will make your viewing experience of the website slow. Many of the blocks on the homepage (to name but a few locations of the site) have been specifically designed based on browser caching, to ensure a fast user experience of our site.
I can guess that you clear the cache and history after every visit to the web, to minimise malware on your machine. Yes that's a very safe approach, though if you have a good internet security suite on your machine, then it should analysis every page before displaying it to you.