When the plumbing is installed in a new home it is usually pressure tested upon completion to make sure there are no leaks. This is the only test that can normally be done since the water usually isn't turned on until the buyer moves in and has the utilities hooked up.
I have found that even though you pressurize water lines with air it is possible that you will not find a leak even though it exists. This is primarily because the water will "wash" at any sealer that has been used on any joints where air will push the sealer in front of it and hold it in place.
For this reason small leaks are sometimes common in new home construction. Normally these leaks occur around threaded joints but can occur in glued joints as well. Normally just taking a wrench and tightening the joints is all that is required. Occasionally new thread sealer will have to be installed.
In a glued joint; however, the joint will have to be cut out and replaced with a new one as there is no way to seal a glued joint without breaking it apart. Most often these types of repairs will be in the basement of under the house. Occasionally leaks of this type will appear around the water heater and hot water lines. This is attributed to the heat of the water as well as the pressure.
Hot water on the left and cold water on the right with cold water going to the toilet. Normally everyone knows this; however, when a plumber is laying on his back under a home it is possible to get your left and right mixed up. Usually you can remedy this condition by just switching the supply tubes under the sink. However if it is a tub or toilet the line will have to be cut and tied in to the correct line.
The only other really common problem with water inlets in a new home is loose fixtures. Maybe a faucet never got tightened all the way or quite possibly the plumber damaged the fixture when installing it.
With the Drain Waste and Vent system in a new home the problems are fewer. Most all problems in the DWV system are either loose connections or improper slope of the drain pipe. The drain pipes in a home should slope 1/4 inch every 10 foot of drain. If you get a low spot it will cause a backup or at least has that potential for such. These low spots are most often caused by the plumber not installing pipe hangers at the proper interval.
When checking your new homes plumbing you should look for obvious leaks when you first have the water hooked up and again in about thirty days. If you have no leaks at this time your water supply is good to go.
To check the DWV system you should close the drain in your tubs and sinks and run water to see if it holds water or not. If it does not leak then open the drain and let the water drain while simultaneously flushing your toilet(s). This will fill the drain pipes underneath the home with water so you can check for leaks and proper drain flow.