Can't copy paste on the first try
This is a known issue for Firefox. Check http://kb.mozillazine.org/Clipboard_not_working.
Section Removing AppInit_DLLS describes a solution to most common reason for delay. Renaming this registry key most probably will resolve the issue (it did for me on Firefox 7.0.1, Windows XP SP3). Check the contents of the same registry key after reboot. If the problem persists, the application that reappeared in the key is the one causing the problem.
Also, make sure the webpage you are accessing is not using keylogging script (which may be a desired behaviour) that blocks the usage of Ctrl+C, Ctrl+V.
This is a very random problem that exists in Windows since always. I normally hit Ctrl-C a couple of times when I want to be sure that the copy is really done. Otherwise, once out of about a dozen copy operation misses out.
However, in your case the frequency of missed-out copies seems to be much higher, this could be caused by some installed product that keeps accessing the clipboard. To copy into the clipboard, Firefox (or any other product) must obtain exclusive access to it, which is impossible if already accessed by some other program.
My first try would be to reboot in Safe mode and see if the problem is resolved. If it is, then some installed product is interfering, and you would need to find out which by trying. Such a product is probably launched during the boot, and a good tool to find and disable/re-enable startup items is Autoruns for Windows, which also can save and restore your current settings.
Any product that touches upon the clipboard is a suspect, especially clipboard extenders and similar.
If this problem only occurs in Firefox, it might be caused by an extension. Invoke "Mozilla Firefox (Safe Mode)" to check this possibility. If that's the case, disable extensions until you find the guilty one.
I suggest to take some precautions, such as creating a system restore point, before monkeying with startup items.