Leaks, at times cannot be verified to be with either the test setup or aircraft. Covering all associated ports/probes and pressurizing the aircraft is a good way to verify aircraft leaks. Static leaks would be indicated by the altimeter driving down. Pitot leaks would cause the airspeed indicator to drive up. Either of these problems would be noted almost right at the beginning of pressure differential increase.
I tend not to trust the newer "totally automatic" pitot/static testers. I have seen "run-a ways" by these testers not being operated correctly. I still prefer the manually operated RVSM digital testers to the automatics. The last time I checked, air data components were mighty expensive to replace. The boss man always enjoys it when he is told a unit got smoked. If you're not totally familiar with an automatic test unit, don't use it.
It should be noted when accomplishing altitude checks that the airspeed indicator Vmo needle will drop as the static system is driven higher. This is proper; overspeed indication is a function of altitude.
Springtime is noted for mud dauber wasp nests in pitot system lines. The usual result of this is an aborted takeoff for airspeed splits. If blockage is suspected, tie into both pitot systems. While watching the airspeed indicators in the cockpit, apply pressure to simulate a quick airspeed climb, if one is slower to increase, it is almost guarantied blockage is present. After the blockage is cleared with wire, blow outboard from the air data or airspeed indicator with nitrogen. Verify no other component is connected to that pitot system before hitting the system with regulated bottle pressure. I would never exceed 50PSI for clearing lines, if the blockage is still present while using higher pressures, a line will split open and require changing.
Pitot/Static tester control valves use nylon seats. It is a good practice to open all the valves after tests have been run. This will keep the seats from warping. Trying to control the tester with leaking valves is very difficult. Opening the valves will also drain the tanks and provide for safe transportation if the unit is to be shipped on an aircraft.