It is my understanding that static pressure port measurements are slightly affected by AOA. To account for this, processing of static pressure raw data includes a correction based on measured AOA. For 737 I believe that static pressure correction for each sensor is based on the AOA vane signal from the same side of the airplane. If one of the vane signals is incorrect, that side's static port pressure signal will be improperly "corrected" and thus read slightly different from the side that has the correct AOA reading. The first result is that altitude as computed based on static pressure will mistrack slightly between left and right.
Pitot pressure is not affected much by variation in AOA so there is no AOA correction applied to that signal. Left and right dynamic pressure readings would be expected to agree. Airspeed, however, is computed based on the difference between pitot and static pressures and thus will be slightly different when comparing the reading from the side of the airplane that has incorrect AOA and thus incorrect static pressure vs. the side that has proper AOA and thus correct static pressure.
The degree of altitude and airspeed disagree left to right will not be severe, but it is interesting to note that one errant AOA signal can yield all of the following:
1. Altitude mis-compare
2. Airspeed mis-compare
3. Stick shaker on one column but not the other
4. Erroneous MCAS if the FCC on the side with the errant AOA is the active one