Also, check out EPA at: http://www.epa.gov/lead/pubs/leadpdfe.pdf. This publication should have been provided to you and the seller by your agents.
When you are in contract you have the opportunity to inspect the intended property, but maybe not the common area...though an inspector may be happy to do so...you have no rights regarding that inspection it would only be for your information.
Regarding 1951, Health officials did not advocate the restriction of lead paint until 1949...but the Federal Government did not ban the use until 1970. It is estimated that 75% of homes built before 1978 contain lead pigment..those built before 1960 can have a concentration of up to 50% lead by weight in the pigment! It is actually the dust that is considered most harmful...that is why it is recommended to have a specialist remove the paint..you can always get more info or references at the National Center for Lead Safe Housing located in Columbia MD 410-964-1230.
Are you in a contract to buy this property? If so, does your contract state that you have the right to have a lead paint test performed? If you are under contract, please ask your agent about your rights under your contract. If you are not sure that your agent has the proper information, go to the broker that the agent works for and ask them to help you. Lead paint is a serious thing for some people, especially if you have children. Years ago, it was realized that the lead levels in paint was so significant that when ingested (especially in children), could cause brain damage. You even need to be very cautious when removing lead paint as not to inhale the dust or fumes. If you are in a contract, you should have received a Lead Paint pamphlet with detailed information provided to you. That is a federal law.
If you are not in a contract to purchase this property, but are very interested, make sure that it is clear in your contract that you want to have the right to perform a lead paint test. Contact several lead paint testing contractors in the area and get pricing for these test prior to getting into the contract to purchase. That way, you have the cost of the test up front and have the right to run the test if you feel that it is necessary. Some home inspectors perform lead tests and some do not. I would make sure that you hire an inspector that does so that all of your concerns can be addressed during one appointment.
My first home had lead paint, and it was never a concern to us because we never had to do any extensive work inside the home on surfaces that had the paint on it. As Chris said below, it is more prevalent on window sills, mouldings, doors and trim work. If the sellers have painted over with latex paint which is the product that has been more widely used since 1978, the lead paint has been covered and does not pose as much of a threat until you sand or strip all of the paint off or if the paint is peeling off. That is where you get the most risk. Young children and babies tend to teeth on things and could ingest the lead paint by chewing on a window will or some trim work in the house. Just be aware of this and keep your children from doing that. It can cause a serious health risk to infants and young children.
The truth is that lead paint was a more durable product and lasted longer than the paint we use today. But the health risk it poses far outweighed it's durablity factor and was removed from the market.
Please feel free to contact me if you have any further questions.