Plaster is no more or less a health concern that drywall provided both are in good condition. That being said here are the areas you would need to consider. Before I comment as a side note, I am not a home inspector. Rather I comment from my experience working with both materials.
Concerns with plaster would be surface conditions (both the plaster and the paint) and substrate. Pealing and flaking paint when the surface was skim coated could if excessive produce dust. For those with allergies this might be an issue. The surface should be repaired and maintained properly. A second and less commonly understood issue is with the substrates or more precisely the 'brown coat'. Jamestown has a lot of older homes. The process used in these homes to plaster was as follows:
1. Install lath board.
2. Apply 'brown coat' or first coat of plaster. This is a cement like coat that at times contained horse hair or other available fiber.
3. Apply second coat. This would be a plaster material.
4. Apply the finish coat of plaster.
After this it would be painted.
When aging several things can occur. The surface or finish coat can begin to break down including cracking. This should be visible unless it was skim coated and painted. A more difficult issue is if the 'brown coat' begins to break down. Two ways to know this potential issue would be 1. An odor. You have hear of some houses having an 'old people' smell even when clean. That is actually the 'brown coat' breaking down including the decay of the fiber. I am not a health expert, but I am unaware of any 'health risk' with this. But I do know that the only what to get rid of the smell is a high quality thorough pain job or removal of the plaster altogether. 2. At times the 'brown coat' breaks away from the lath. When originally applied the material was worked into the lath and this created a way for the 'brown coat' to 'hook' onto the lath. At times during breakdown the plaster 'fingers' that wrap over the lath break. What you get is sections of plaster that are not secure. To test for this we normally just walk along the wall tapping the wall to find if there are 'hollow' spots. Larger cracks can also indicate plaster breaking away from the lath.
You should get a home inspection when you do a purchase. When calling inspectors prior to hiring ask them what there knowledge of plaster walls is. A realtor in Chautauqua County should have at least some knowledge of plaster walls as most of the city housing stock is older. Your agent should be able to help with some initial questions. We are however not home inspectors nor health professionals. Depending on your concerns and the visual conditions recommendations can be made.
To your success in finding a home that fills your needs.
(Sorry for the long explanation. But I love both real estate and construction!)
You might note on the EPA's page on the right is a section called 'Key Information'. It points out the the 'best practice' is, if its in good condition leave it alone. In most cases this is the right thing to do. A certified asbestos contractor/inspector can help if you feel the need to go that route. It should also be noted that asbestos was used in many building materials. The EPA site mentions some possibilities. You will also find information on encapsulation and encasement.
The real issue with asbestos is when it is disturbed. It's when a remodeling project is planned that risk rises. In all construction projects where dust and debris is a factor, proper breathing and ventilation devices should be used. Even modern plaster can contain substances such as gypsum. Cement products can contain silica. Both these substances are harmful if inhaled.
Any remediation project may have several potential solutions. And while real estate agents and inspectors can help with some input, others certified in a particular area may be needed. The final decision on how or to cure rest with the buyer/seller/owner.
(I am not a home inspector or an asbestos professional. These comments are general in nature.)