MattyMo's advice will get you off to a good start. Here's another person's pic of that filter you need to check.
There is also the screen on the petcock inside the tank, but I'd exhaust the other checks before bothering with that.
The crack-the-gas-cap trick will tell you if it's a clogged breather tube, but you might as well get under there and check/modify the breather tubes for the tank and carbs:
If it is on the electrical side of things, start with the easy stuff like clean and dielectric grease the connectors(everything, but particularly the spark plug wires and the wires feeding the coils), coil check(resistance checks), spark check.
Not quite in line with your symptoms, more of a problem at lower speeds when they go bad, but check the vacuum caps/lines while going over everything. 4 nipples to check total, 1 carb side and 1 manifold side for each carb. Still have the air injector system on it?