To remove most dust without moving the knobs, best way I have found for light to medium dust is a vacuum cleaner with a bristle brush. I also use a feather duster sometimes, not the kind with feathers but the synthetic bristle hair type, it also allows dusting channel strips without altering the knob settings. For tighter areas I use a keyboard cleaner, kind for a computer keyboard, it's also synthetic hair type, but smaller with finer hairs. For panels and display surfaces I often use Endust spray and than dust, that helps keep the dust from floating around and settling back down, but just spraying Endust on a clean rag and wiping around the knobs if you don't need to keep them set will do the job. For pots, contacts and circuits, if you are in a country that hasn't banned Freon 22 based cleaners, they are some of the best, they evaporate oils and stuff in tight spots where you can't physically wipe and with great benefit of it being 100% non-conductive, you don't have to worry about shorts and can even clean circuits that you don't want to power off. It's an excellent inside the pot cleaner. It's banned in the USA without a special license due to the ozone layer threat and latest EPA regulations, for example air conditioner repair men for recharging ac's or auto-mechanics that are licensed to recharge auto ac's. I think most of the auto ac's are using a substitute now a days that doesn't have the PCB's, but the ac guys can still get the F22. You can also buy the spray cans in Mexico. I always pick up a few cans when I'm down there, but you aren't supposed to bring it into the US, so that's a call on your part.
You can use a "slightly" damp rag if you are careful, but I don't blame the tech for being paranoid. A damp rag is good for grime, smudge and fingerprints, but for dust it just globs it and makes it harder to vacuum or dust off. For channel marking adhesive tape residue, such as the off white masking tape that you mark instruments on each channel with, a compound called Oops works good on metal parts, but if you use it on plastic parts, be sure to test a small area first, it doesn't agree with cheaper type plastics. Oops is about the only thing that I've found that gets the hard core Chinese duct tape residue off of surfaces, such as cables that I have to tape down at a live remote. I use it to clean my mouse and surfaces on DAW's too. You can buy it at Wal-Mart type stores.