To check the AAP, simply pull the vac line off it and see if there is gas in the line. If so, the diaphram is punctured and needs to be replaced. The AAP really only affects you when the engine is cold and you first step on the gas. It squirts a little extra fuel in for ya. Probably not your problem as I'm assuming this happens when the engine is warm as well?

The fuel filter is clipped to the inside of the frame right near the gas tank. Just follow the lines off the tank and one will lead you there quickly. Its a 2min replacement - very easy.

Now for your sputtering problem.. does this happen when warm or cold or both? I'm gonna guess warm and not cold - if so I bet your choke is not opening. This would cause the carb to dump too rich a mixture in the engine and cause it to flood/sputter. Which would explain why it only happens under acceleration - you're probably flooring the pedal dumping too much gas without any air.

To tell if your choke is opening - let the engine warm up to temp, pull the air cleaner cover off, and look at the top fo the carb. Ignore the drivers side choke plate - it is vacum operated and does its own thing. What you want to look at is the passenger side choke plate - it should be compeltely vertical. If it is not, then this is your problem.

Annnd thats the first thing I would check (again let us know what temperature this happens at as I'm currently guessing). I can probably come up with some more stuff to look at too..

-Scerb