We would advise you to contact a lawyer to find out if driving with expired registration / tags / plates in the District of Columbia is an offense which can cause the police to arrest you. We have read several reports that people have been arrested even for their DC registration only being expired for a few days but then were released after paying a $50 fine.
Laws and the way in which the District of Columbia allows the Metropolitan Police Department (MPD) to enforce them do change so a lawyer or even the DC DMV should be able to give you the most up to date and correct information.
We can give you this information which may help you understand the portion of law you were cited under. According to Section 50-1501.04 of the Washington DC Code it is unlawful to operate a vehicle upon any public highway of DC if the vehicle is not registered. The motor vehicle also needs to have attached and displayed identification tags. It is unlawful in DC for the owner of any motor vehicle to knowingly permit the operation of a vehicle that is not properly registered (thus have expired tags as you mentioned).
The penalties mentioned in subsection (b)(1) include a fine of not more than $1000 or imprisonment of not more than 30 days or both fine and imprisonment upon being convicted of the offense. It is noted that all such prosecutions shall be in the Superior Court of the District of Columbia upon information filed by the Corporation Counsel of the District of Columbia or any of his assistants in the name of the District of Columbia.
This part of the DC Code also states that if a motor vehicle is being used knowingly with a counterfeit, stolen or otherwise fraudulent temporary identification tag than the car may be subject to seizure by the Mayor or any law enforcement officer of the District and to forfeiture to the District. This penalty is in addition to the fine or imprisonment that was already mentioned.
Since you were not arrested we would assume you were given a court date. If this is the case then try contacting the court to see if by renewing your tags (registration) before the court date you can help lower the penalties that will be accessed. If you can then get your plates up to date as soon as possible and take evidence of this to the court.
As for points, District of Columbia drivers receive points for certain moving traffic violations, whether the violations occur in the District of Columbia or in other states. DMV assesses points if you are found liable at a hearing, fail to pay a ticket within the time required, are convicted in court of a traffic violation, or you pay the ticket (payment is an admission of liability). The number of points you will receive depends on the type of violation. We did not see points assigned to the offense of driving with expired registration which is usual. In many states since this is not considered a moving violation and thus is not assessed points.
To find out for certain if any points will be put on your DC driving record contact the DC DMV. Even if no points are placed on your driver's history you will want to see if the conviction of driving with expired registration will be and if so how long it will remain.