My comptuer mouse (or to be exact, cursor) seems to have developed a mind of its own, occasionally clicks on things by itself and cursor whizzes off.

More likely to be hardware or software problem? What d'ya think?

To be on the safe side, I've run anti-virus, anti-malware etc. but no difference.

is it wireless?
if so, its probably interferance at one end of the connection (could be transmitter, or reciever)
if its optical mouse, they can be confused by some surfaces too, especially by vibration.

while watching films on our media pc build, we have to put the mouse on the carpet, as the sound system makes the table buzz a little, and the mouse goes apepoop

Is it an infrared mouse? could there be some interference from another ir device close by?

It's an optical mouse and I have to admit it's being used on a rather stained archaeological mouse mat (it's worked ok on it for months tho). I'll give the desk surface a good clean and try it on there.

Cheers.