Oh I hate it when people keep taking me seriously.
In theory, static pressure is the pressure you'd sense if sat stationary in a balloon at the same point and altitude. So, it shouldn't change with speed - it's pitot (dynamic) pressure that changes with speed.
That's the theory, and no doubt most textbooks say that. In practice unbelievable amounts of effort goes into finding the one spot on the airframe where you can put a static port to get that - I've seen on the side of the fuselage, on the side of the fin, a spot on a strut, under the belly, behind a "static dam" (fancy name for a small block of wood glued to the aeroplane).
In practice you'll never quite achieve constant static pressure with airspeed - this is the reason that most aeroplanes have in the approved POH a CAS (or EAS) .v. IAS graph. Good ones (and with any luck anything certified to part 23 or 25) should have no more than 5kn error through most of the full range except down at low speeds where putting the pitot to high angles of attack tends to mask any static problems. However, I've certainly seen 15-20% airspeed error which with a low speed aeroplane means 100-300ft altitude error - these errors however tend to be seen on aeroplanes not properly sorted, which means homebuilts, microlights, historic aircraft and prototypes that we're still working on.
From an "ordinary" pilots viewpoint then static pressure is constant FOR A GIVEN PRESSURE ALTITUDE. From an engineers viewpoint (or a test pilots) we will spend many happy days in the flight test department trying to make that true.