I have all relevant/latest updates for Firefox & IE8 & WinXP, and am not having any trouble viewing YouTube with either one.
I've been using a (free) utility, Secunia PSI, to check what software subsystems (Java, Flash, etc.) may need updates.
Regards to Java, older versions are not automatically uninstalled when updates are done, but the recommendation is that they *should* be manually uninstalled. Look through your Add/Remove Programs and uninstall old versions (can't say if that'll help your problem, but it's good housekeeping).