A little dust, in and of itself, will probably not hurt your speakers. Sound will not be affected (unless its caked on mud or something). Tar and nicotine isn't as much of a problem today, as Dr Fred says.
I have carpeted speakers and it's not uncommon for my white-haired cat to decide she wants to sleep on them. So a lint roller is always around. You can also carry a can of compressed air if they are starting to look unsightly on the job.
As far as mikes are concerned, I've actually seen a gadget that you can hook to your mike stand or TV stand. When a singer picks up a mike to sing, it sprays the mike with an anti bacteriant. Don't know whether that's good for the mike or not, but it will probably sell in this day and age of H1N1.