My husband was in the dental repair field and used to do repairs in dentist's offices. He'd sometimes have to stick his hands in some pretty gross places (think all you spit and all that's vacuumed out of your mouth) to do repairs. He knew who was a clean dentist and who wasn't, he told me there were dentists who would come in to check on the progess of a repair, shake my husband's nasty hand (both of them gloved) and then walk back in to work on a client's mouth without changing gloves; he'd see dentists go from one client to another without changing gloves. There are no regular inspections, and there are dentist who don't clean the important stuff well, who don't make sure whoever is sterilizing the equipment is doing their job well. There are standards they're supposed to adhere to, but no one checks. You really should see your dentist put clean gloves on before he works on you (the hygenist, too).
If the office is that dirty, I'd RUN. He's not even bothering to put up the facade that he runs a clean operation. If he doesn't care enough about whether his clients wonder if the place ever gets cleaned, then I'd suspect he doesn't care if they wonder if his equipment is clean and in good repair. Blech.
Edit: I want to edit this to say I'm not trashing dentists; there are many many many good dentists - but just like anything you buy and any service you hire, it is caveat emptor.