When buying a moped its important to check for the following things:
Sellers history on ebay - check feedback
Size of engine
Stroke engine size
If the bike is registered in the UK and has relevant forms for registration (e.g, EEC, COC for if the bike is imported)
If the seller offers any warranty on the bike
If the bike can be insured in the UK, some sellers have details on the advert of insurance brokers that can insure the bike at a cheap cost.
I myself sell mopeds on Ebay and know what you should be looking out for when buying a moped.