I noticed that my plastic PCR Vader helmet has a lot of spots built up on it recently. Any tips on what cleaning solutions would be good to remove them?

I don't think anything exotic would be needed just a dampened soft clean cloth then wipe it down afterward with a soft dry cloth to clean up excess moisture (dry end of the same cloth?). If you need to go so far as using soap I would just use a drop of dish soap in some water then use that to dampen the cloth, then wipe it down again with soap-free water, then dry it.

That is from dust settling for extended period. I usually use polish on my helmets to help retain the paint finish.