I prefer a concrete slab foundation over pier and beam. I've never lived where they have basements, and I don't have any experience with basements, so I can't comment on that. I also wont get into the pros and cons over one or the other on new construction. What I will say is that if the slab is in good shape, then there shouldn't be anything to worry about. The concern with a slab foundation is movement in the soil that results in cracking of the slab. This is impossible to fix, and very expensive to minimize. Usually the repairs last a few years and then it starts all over again. You need to do a very detailed inspection of the flooring and sheetrock. Cracks in the sheetrock can be from a poor roof design, or somebody cutting away supporting lumber in the roof for plumbing or AC ducts, so don't assume sheetrock cracks are foundation related. Be sure to look all around the exterior of the slab. It should be exposed. If it's covered in dirt, remove the dirt and look. This is also the number one way termites get into the walls, so if there is dirt covering the slab, it needs to be removed anyway. If the slab is bad, you will see it there. Then you need to decide if you want to deal with that money pit or move on.
As for the plumbing going through the slab, if everything is still working after all these years, you should be fine. I like houses built in the 70's. They are usually ugly, but the wood and materials used are all heavy duty, high quality. In the 80's, the EPA took over and made everything a mess with new regulations that gave us pressboard, plastic and glue that never held. Just try removing the wallpaper on a house from the 70's compared to one in the 80's. That glue they used back then is permanent!!! In the 90's things started getting better as manufacturers stared to standardize things and quality improved.
If you do have a leak under the slab, it's pretty easy to cut it out with a diamond blade saw and SDS Max rotary hammer. I do this all the time when remodeling a house. It's a mess, and you need to redo the flooring, but pretty straight forward with the right tools. Finding the leak is where it gets interesting. On some of the jobs I've done, instead of cutting open the floor trying to find it, I just cap the line, then run PEX up the wall, through the attic and down the wall where it needs to be. This is usually a day job, plus repairing the walls, or replacing what was in front of the wall.
Eddie