So I finally decided to invest in a guitar... or my neighbor happened to leave the country, and wanted to get rid of some stuff. One of the above. In any case, I now have a complete electric guitar set including amplifier.
The amplifier did not work all that well, sadly. A couple of the knobs needed fiddling forever to get some sound out of it. A bit like trying to open a safe without knowing the combination.
The solution was simple though. In fact, it's almost embarrassing to make a blog post about it. The answer is called "contact spray".
The above is the kind you find in the Netherlands, but I'm sure other countries have equivalent types.
The spray improves the contact by dissolving dust and oxidation, in this case between the contact surfaces in the potentiometers. Just pulling off the knobs and spraying might work, but to reach from every angle (and for the fun of it) I opened it up.
Some spraying and knob-turning later, it worked fine! Interesting to note is that the smooth feeling when turning the knobs disappeared, and in one case it became much harder to turn. My guess is that the spray dissolves any oil or fat put there as lubricant.
To fill out an otherwise tiny post, below you can see the part that creates the reverb (a sound affect which sounds a bit like echo). It was a surprise to me that this was a mechanical part, instead of some electronic circuit. It works quite simply by inducing vibrations on one side of the springs with electromagnets, and reading the vibrations on the other side with the same mechanism.
One detail remains. Learning how to play the guitar.
EDIT
A friend of mine who has worked as a sound guy for a long time pointed out to me that there are better ways to fix the problem. As I suspected, the contact spray I use dissolves the existing lubricant, which removes the smooth feeling, but also risks damaging the carbon when turning, which could decrease the life time of the potentiometer. I've also noticed that, although the knobs work, there is quite some noise while turning.
Apparently there are special lubricants that takes care of those issues. They are quite expensive, but I suppose when a mixer board costs thousands of Euros it's a small price to pay. Here is some advice and information on how to properly clean knobs and faders. Last resort, if it still does not work properly, would of course be to replace the potentiometers.