We moved in about 8 months ago. Right away, I noticed that the dishwasher leaves a white film on some things, namely plastic plates. A few months in, I noticed it didn't sound right (like the water sprays were blocked and trickling) and it was looking really grimy on the inside. I disassembled the filters and grates and found it completely blocked with sludge. I cleaned the black scum from the walls of the machine with vinegar (it was black and waxy), and soaked the filters, scrubbing them completely clean. I then ran a cycle empty with a dishwasher cleaning kit. Seemed to fix the problem. Another month or so goes by, and I have to do the same thing AGAIN, though to a lesser extent. Again, I ran an empty cycle with a cleaning kit. So we've gotten better at making sure dishes are thoroughly rinsed before being loaded, but even so, the filters are getting clogged and sludgy, and there's black grime and mold on the interior walls. In 8 months, I've had to do this THREE separate times, and I'll have to do it again in a few days. Granted, I've cleaned a dishwasher before, but is it normal to need to with this kind of frequency? What am I doing wrong?

but is it normal to need to with this kind of frequency?
No.

Unless you see the same kind of residue in other places such as a bath tub I would say that you something wrong in the dishwasher. A dishwasher is really nothing more than a water pump. It lets water , pumps it around for while and then pumps it out. I would guess that the impeller of the pump is some kind of black plastic and is rubbing against something and wearing away.

Best to just replace dishwasher.