When I have a little extra time before departure I actually take a few minutes to clean the centre console, glareshield and so on. A couple of wet wipes can do wonders. Also, if the cleaners are still on the aircraft when I get on ( usually the case nowadays...) they are more than happy to pop in with their vacuum cleaner to do the carpeting.
Some of the stains are fairly permanent , especially the ones on the commonly used switches so not much one can do about those.
You're right about the engineers. They are very overworked - we're lucky to have someone clear the snags let alone clean the flight deck. At this rate we'll probably soon get authority to sign off the aircraft ourselves..................