Main point is to be careful where you put the probe flying lead croc clip. It is already connected to earth AND the computer case is likely earthed too. So putting it on the case or a mounting screw, no problem. Putting it on a point with a voltage could send a lot of current through your scope and damage it. (Computer PSUs can deliver up to 40A)
If there is no need for high accuracy then I often just tie the croc clip back to the probe coax and rely in the fact that the scope is already grounded. Or, put one probe croc clip on the case and use the other probe ungrounded. The only time this isn't ideal is when measuring small or fast signals, when having a local ground can make them cleaner.
Other point, if using an uncapped probe beware that the metal ring behind the tip is grounded, and I couldn't count the number of times I've seen equipment blown up by a probe slip allowing this to short something out.
If you don't have a cover for it (the decent probe kits come with one) put some tape round it.
HTH.