I use Firefox with Win 7 64 bit no problems. Firefox is the x86 or 32 bit version however, as is my version of IE, there are problems with Adobe Flash not supporting 64 bit architecture so 64bit browsers won't support a lot of Flash enabled sites.
The x86 or 32bit Firefox and IE browsers work fine with Win 7 64bit, I've never had problems with either.
No problems, it's a mistake anyone could make. A great deal of software is still 32bit as opposed to 64bit as most computers are still 32bit based, I believe this will change in the future though as more and more systems are based around 64bit as it allows for larger amounts of RAM to be used.
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