When Professor Umbridge becomes Hogwarts High Inquisitor, she proceeded to hold inspections of all the other Hogwarts teachers to assess whether or not they are 'up to scratch'. However, despite the fact that Harry, Ron and Hermione mentioned several times that they looked forward to seeing Professor Binns' class being inspected ('Bet Umbridge is in History of Magic,' said Ron grimly, as they set off for Binns's lesson. 'She hasn't inspected Binns yet ... bet you anything she's there ...'), it appears that Professor Umbridge never bothered. I was curious why? Seems interesting to have the main characters mention it twice and then give no reason why it never occurrs.
You have to remember that Hogwarts has 7 different years worth of students, from 4 different houses. Each class seemingly is taken by 2 houses at once, though it is possible that some are taught to more or less depending on attendance (i.e. when the students get older and can select their own courses). Assuming Professor Binns' teaches at least one course to each of the 7 years, this gives us (approximately) 14 courses total that he will be teaching (7 * 2). Harry had already witnessed Umbridge inspecting several teachers, and it seems unlikely that he would end up witnessing all of the inspections.
Also as @AnthonyGrist pointed out in his comment, it is unlikely that an inspection of Binns' class would be interesting in the least. He is known to be a bore, and teaches History. Professor Umbridge was more concerned with dispelling rumors about Voldemort and the present rather than facts about the past.
So in conclusion, it is safe to assume that Umbridge did inspect Professor Binns' class, but that it was (as expected) dull and uneventful, and therefore unworthy of discussing in the books. Especially since it seems unlikely that Harry even witnessed the inspection himself.