I recently managed to get the moped running properly, albeit for only a short time. Things were looking up: I replaced the spark plug, cleaned out the exhaust, adjusted the idle / fuel screws, and even replaced the brakes (I can stop now!).

So everything was looking good. I was test-riding it after a short hiatus, and the moped was running fine. Near the end of my ride, I stopped at an intersection to make a left turn. I revved the engine while still stationary in anticipation of the light turning green -- I didn't want to hold up traffic, and the 50cc engine takes a while to get going. I pushed off from standstill, the scooter started moving fine, but soon thereafter started lagging. It absolutely refused to go past 20 MPH even though I'd usually go 27-28 on the same stretch of road. It was consistently going slower afterwards, and I scurried back home as best as I could.

I've revved the engine like this in the past (with the moped stationary), but for shorter durations. This time I'd say I was on full throttle ~5-10 seconds while stationary.

A couple of days later I fired it up, but it ran horribly. I managed to get it moving, but it hit 10-12 MPH on mostly flat land (where 27 MPH was common). It felt as if the engine was providing power for a couple of seconds, then stopped the power delivery for a couple of seconds, and it kept doing this over and over. It was so weak that I had to push it up a hill to get it back to my residence.

I thought -- for just a second -- that I smelled a burning clutch when I was riding it back home after the intersection incident. After I got home, I "smelled" around, but couldn't pick up any burnt clutch scent.

I sincerely hope the clutch isn't the culprit, since it's an expensive fix. Please let me know if you have any ideas as to where I can start troubleshooting (aside from the clutch, of course), as the weather's nice and I'm hoping to get it going this weekend -- fingers crossed!

7/10/10 Update

I swear guys, I'm not crazy. There was a problem with the moped.

This morning I fired it up the usual way, hoping to analyze how it runs. It hit 29 MPH on flat land like nobody's business and I rode it around for a good half hour with no problems. I have no idea what changed in the last couple of weeks -- perhaps it had some time to think about its problems and resolved them.

I have a feeling this won't be the last time this problem pops up. I will most likely be coming back to this post sometime in the future :)

Thanks for all the replies!