Those are A35 sprints are good bikes and there aren't really any real downsides. Your checklist is going to be basically the same as any other moped. Most minor issues are really price negotiating points more than anything else.
• Paperwork: If your state requires a title, make sure that is in order, and that the title matches the number on the frame.
• Frame: Is the tank rusty, are the vin decals in place, is the vin stamped into the right side motor mount? Some models only had the vin number on foil decals which fall off, fade or get worn through due to cable rub, etc.
• Signs of a wreck : Bent forks, damage to fork stop, large dents in the frame.
• General wear: Side to side slop in the swing-arm bushings. I don't think anyone ever greased these so if it doesn't have any major slop you know it has fairly low miles or has been well maintained. Sit on the bike and hold the front brake, now rock the bike back and forth with your feet, can you feel slop in the fork lowers or the steering head?
•Motor: Does the motor turn, have compression, or Run? Is the area around the drive sprocket and rear hub coated in oil or grease? If it's wet, oil is leaking around the pedal/kick shaft.
•If it runs and drives: Does the motor accelerate and shift well, or does it struggle to shift and chatter. Does it smoke heavily. This could be a rich oil mix, but heavy smoke is often a sign of a leaking crank seal on the transmission side. These motors aren't difficult to rebuild and you can still get most of the important parts. They are common enough that used parts shouldn't be a problem to find either.