The most common problem with plumbing in an older home is that the sewer lines from the house to the sewer main that the City owns are broken, blocked or clogged.
Older sewer lines that run from under the house - usually under the slab - to the sewer main at the street are almost always made of clay or cast iron pipe. Clay pipe not only breaks easily from movement, it can easily be broken and invaded by tree roots. Cast iron deteriorates over time. The life span of clay and cast iron pipes is 25 -35 years. So if you are looking at a home that old or older, you should consider this possibility. Think your Oak Tree isn't alive? Well, somehow, oak roots know how to break and enter into sewer lines to syphon off the water inside.
Sometimes the clay or cast iron pipe is damaged from the expansive clay soils in Texas. Sometimes the slab itself moves and breaks the pipe that is entering the vertical penetration through the slab. There can be a number of ways that the sewer lines are broken, blocked or clogged. When sewer lines do break, soil collapses in and the flow of refuse to the city main is interrupted. If that blockage is under the slab, then water can pool under the slab and cause deflection or breakage of the slab above. So it isn't just sewer lines that are affected.
So what can you do about broken sewer lines? Will the ordinary home inspection detect this? No, the ordinary home inspection will probably not discover whether you have broken sewer lines or not. There are signs and symptoms of broken sewer lines such as slow flow, backups and sewer gas smells. But those can be hard to catch on a one time two hour home inspection.
To be sure whether you have good sewer lines, you probably need to have a camera inspection of the lines. Or you could do a hydrostatic test but if your hydrostatic test fails, you for sure have to have the lines filmed to know what's wrong.
Of course if the hydrostatic test fails, you could punt on that house. But if you like the charm and location of an older neighborhood like Alamo Heights or West University Place, you are going to have this problem head on. The expense is worth it and you can negotiate the repairs into the sale.