Does the pressure at the static ports drop as the aircraft's speed increases?
The comment:  


  In fact, the pressure at the static ports will drop as the aircraft's
  speed increases (Bernoulli principle)


is not exactly accurate. The aircraft is a complex aerodynamic shape and static pressure distribution across the fuselage is not linear. An example is provided by the following figure from NASA Technical Memorandum 104316:  

  

[Source: NASA]  

If you look at the graphical part of the above figure, you'll see areas where the pressure is above (>0) and below (&lt;0) the reference pressure. As the airspeed increases, the tendency will be for the positive values to get bigger and the negative values to get lower (more negative). So along the line between points 2 and 3, and also between 4 and 5 (over the wing), the pressure will drop as speed increases. Between 1 and 2 (the nose), and between 3 and 4 (just in front of the wing), the pressures will rise with speed.

From the same report:  


  Zero static pressure error on the fuselage exists at locations 2
  through 5. One of these locations is chosen for the static port. To
  keep pneumatic lag small, the static port is normally located as near
  the airdata instruments as possible (or the other way around). (To
  determine this location precisely, several static ports are made in
  this area. The optimum location is then selected as a result of
  comparing the various ports with a reference source, such as a
  trailing cone.) This pressure distribution changes with flight
  condition, so a calibration over the flight envelope may still be
  necessary.
  ...
  Even with the selection of the best static port position, some
  pressure errors will remain, and these errors must be determined in
  flight. The difference between the locally measured static pressure
  and the ambient static pressure, which is dependent upon angle of
  attack, airspeed, and aircraft configuration, is called position
  error.


Based on the measured position error, a Static Source Error Correction (SSEC) table is developed. The SSEC is loaded into the air data system when it is installed in the aircraft so that it can make the necessary corrections.