Never have delt with a Minarelli, but here are the following things to do with any used moped:
1. Clean the carb. Take it apart and wash/swirl it in gas. Then dry everything off and put back together.
2. Remove all carbon. Most peds get carbon on the head and piston. If black/dark brown, use steel wool and remove it until you can see the original color.
3. Change the Plug. Use an Autolite 425, NGK B6HS, ND W20FS-U, Bosch W9EO or Champion L86C. Put the gap at I believe .26 - .28mm
4. Change the fuel line and petcock. Use 3/16" Nitrile or Tygon fuel line, it will last the longest. Also use a fuel filter or two. Also, replace the petcock, sometimes the filter on it corrodes and lets rust build up. Save time and buy one.
Try tightening the nuts on the engine studs. After that, if it still doesn't run properly, adjust the carburetor and check the electrical like Mark said.