Just a preface: I don't know very much about working on bikes, so please don't assume I know anything. Basically, talk to me like I'm an alien that doesn't understand Earth transportation mechanics.
My Georgie is a 2007 S40 that's got 8,323 miles on it (660 of which my husband and I put on since mid-March). It seems like the bike had only one previous owner and I really don't know what he did to the bike, other than superficial stuff (wrapped exhaust, flipped the steering stem upside down). I honestly can't tell if it's got the stock petcock or not. The bike is mostly reliable, especially after I refilled the battery with distilled water (I hope that was the right thing to do!).
So, for the last work week, my husband has been riding my bike due to a flat on his bike (he doesn't have a car). He's noticed some funny things about Georgie. His belt seems squeaky, for one, but I've seen some threads on this and I think it just need to be realigned. Hubs seems really concerned about the popping/backfiring on acceleration, as well as the sputtering/loss of power over 60 mph. I know the backfiring on decel is due to the lean mixture of the carb, but what about on acceleration? I've never messed with the carb and I don't know if the previous owner ever did maintenance on it.