Waggle the jack plug in the input socket of the amp in fact check all the inputs if it has more than one socket and make sure the connections aren't intermittent. If they are this is usually an easy fault to rectify but can be a bit awkward depending on the amp. Next.....

You may or may not want to do this but if the guitar amp uses tubes and they're accessible, (although the chances they won't) gently tap the glass with a pencil and listen for strange crackles and echo noises (microphonics). Once again, there will be some noise but it shouldn't excessive. I know it might be obvious to say but tubes do run very hot so beware – don't touch with your fingers! As far as electric shock goes there shouldn't be any exposed connections accessible without taking the chassis right out of the cabinet which you DEFINITETY WON'T be doing . If there are, then the amp has been modified in some way (badly) which is another indication that perhaps you shouldn't part with your cash. Next.....

How does the amplifier sound to you? Do you like the sound? Just because it's a great make and model doesn't mean you like the way it sounds. Make up your own mind on this. Next.....

Check all operations like channel switching via front panel and/or foot switch and effects, like reverb and delay. All these things should be obvious if they're working or not. Next.....

If the guitar amp you're looking at is a combo (has a built in speaker) check that the speaker isn't buzzy or distorted. Although speakers are easily replaced, they are expensive. Play right up and down the fret board, this will help to see if the speaker distorts at different frequencies. Play LOUD, and play really softly as well. A speaker with a damaged cone might well 'flap' at high volumes, but a speaker with a misaligned coil and cone will sound distorted or sizzy at very low volume levels. Next.....

Make sure the speaker cone is intact, without rips or damage. Take a torch, it'll help you see through the grille : )

Very often private sellers won't give you any sort of guarantee with an amp, but it's worth asking if he/she would give you an option to return the amp within the first week if some nasty fault shows up. If you're buying from a dealer then ask for 3 months or so.

Last but not least. Take your time with all this because the longer the guitar amp is switched on the more chance of it showing up some faults, so don't be in a hurry. If the seller is pushing you along then be suspicious.

Good luck and have fun. Hope you get the Used Guitar Amp you really want!