Your spedometer is mechanical. Verify that the cable is not broken. Second, disconnect the cable from your wheel, and hook it up to a drill --does the spedometer work? If so, the drive on your front wheel is probably shot.
Call your local Honda motorcycle dealer for parts as you need them --they might not be available anymore (I know I can't get spedo cables for my PA50 anymore).
An alternative: put a digital bicycle computer on your moped. Digital spedometers are <b>way</b> more accurate, they keep track of your maximum speed, average speed, and best of all --they have a trip odometer function which is great for keeping track of fuel.
I think the popping you hear in your muffler is just a result of drilling holes in it. If you've ever driven a car with a bad exhaust, it'll make some pretty surprising noises that you probably didn't realize it made. Cover up the holes if you want your moped to stop farting.