Here are the VIRGINIA laws, all annotations denote the section of the CODE OF VIRGINIA (§) or the VIRGINIA ADMINSTRATIVE CODE (VAC) that the law can be found in.

DEFINITIONS:
Virginia does not define a scooter per se, a scooter is either a motorcycle or it is is a moped. There are no in betweens, no ifs, ands, or buts.

A "Motorcycle" is any two-wheeled vehicle (§ 46.2-100). Except when it's a moped.

A "Moped" is any vehicle that has an engine size of 50cc or less, produces no more than 2 bhp, and can travel not more than 30 mph (§ 46.2-100), the pedal restriction was removed in 1998. If you have derestricted your bike so that it goes faster than 30 mph, it is a motorcycle (§ 46.2-914).

If your dealer has derestricted your bike and told you it is still a moped, then THEY ARE LYING. I know at least three local dealers who have done this. One dealer in Leesburg was given thousands of dollars in fines as a result.

DRIVERS LICENSE:
You must have a driver's license with an M-class endorsement to drive a motorcycle (§ 46.2-337). It is a $300 fine, and you may be arrested if you drive a motorcycle without the proper motorcycle license in Virginia, this is the same penalty as driving a car without a license. Anyone 15 1/2 or older may get a motorcycle learner's permit. Anyone who is 16 years old or older, who has held a motorcycle learner's permit for a minimum of 30 days may get a full motorcycle license.

Virginia offers Motorcycle Safety Foundation courses for both beginner's and advanced riders. Successful completion of the beginner's class may be used in place of the driver's license road test. The MSF provides small motorcycles for the beginner's class. You do not need to know how to ride before taking the beginner's class (though having a clue helps). The Advanced class is available to riders with at least 5,000 miles of experience. You may ride your own (inspected, Virginia-registered) scooter in this course. For more info on MSF classes call 888-826-7584 or visit http://www.Learn2Ride.com Keep in mind that classes fill up at least six months in advance, so plan early (or be willing to travel to less congested southern Virginia) if you wish to take one of these courses.

You do not have to have a driver's license to ride a moped (§ 46.2 100
& § 46.2-300). Thus drunks who have had their licenses revoked, may ride mopeds in Virginia. However you must be at least 16 years old to ride a moped (§ 46.2-914).

REGISTRATION:
All motorcycles in Virginia must have a title and display a license plate (§ 46.2-613-1). Motorcycles over 25 years old may display antique historic plates.

Mopeds do not by state law require a license plate. However each moped is require to display a permanent decal or sticker which states "its motor is rated at no more than two brake horsepower producing only ordinary speeds up to a maximum of thirty five miles per hour" (§ 46.2-915). And each city and county in Virginia may decide on its own to require license plates on mopeds (§ 15.2-1720).

INSURANCE:
All motorcycles are required to either carry a liability insurance policy or they are required to pay to state uninsured vehicle fee (§ 46.2-707).

Mopeds do not require insurance.

INSPECTION:
Motorcycles must pass an annual vehicle safety inspection (§ 46.2-1157) unless the motorcycle has historic plates. Motorcycles do not require emissions inspection. The inspection sticker must be displayed on the left front fork (19VAC30-70-50), yes I know, classic Vespas have no left fork.

Mopeds do not require inspection.

HELMETS:
Motorcyclists must wear helmets and eye protection (§ 46.2-910) unless they are riding in a parade.

Moped riders do not need a helmet or eye protection.

OPERATION:
Motorcycles are subject to all highway laws of the state of Virginia. However, motorcycles may use HOV/Car Pool lanes with only one rider (§ 33.1-46.2). Bikes with historic plates may not be used for commuting to work (46.2-730).

A moped is a vehicle subject to all highway laws of the state of Virginia (§ 46.2-800). You may only ride a moped in the right lane (§ 46.2-905).

PARKING:
As a general rule, all parking regulations are local ordinances and not state code. However, according to the Virginia Administrative Code, regulation 8VAC105-10-520 Parking enforcement: "Mopeds may be parked only at bicycle parking racks. Motorcycles may not be parked in
bicycle racks." If you park your bike on a sidewalk and it gets towed...

FREEWAYS:
Any motorcycle that can safely keep up with traffic is allowed on a freeway or interstate.

Mopeds are not allowed on freeways.

Those are the laws. Whether the police choose to enforce them or you choose to obey them is a different story. If you don't like the laws fine. Act on everything you learned in your high school civics class. Write your councilmembers, delegates, senators, and representatives
and ask to change the laws.