Good question:
First thing, visually look at pitot/static probe: Rule-of-thumb, they should be ~parallel with bottom of wing, and the pitot (hole-in-the-front) probe should be parallel with the static (holes-in-the-sides) probe. Also check for cracked metal or plastic tubes. Some aircraft have statics on the bootcowl or fuselage sides, but this isn't typical of Supercubs. I'm amazed at how many ragwing Pipers I've preflighted have problems in this area.
More likely, check airspeed (and altimeter) static hose connections, largely behind the panel. I've seem some dumping to the cockpit, not the official static connections. Frequently the tygon (or whatever) connections have come loose somewhere in th the line. You should trace it all the way back. from the instrument to the pressure/static source. Sometimes some flakey "Y" connections behind the panel, or cracked connectors.
Another related check, see what happens when you open the window/door in flight. If ASI changes, something's wrong with the plumbing, probably ASI static to cockpit or somewhere.
Third thing, I'd drag a GPS along, and compare with the other 'cub.
This effect sometimes also shows up as flakey rate-of-climb indications, if so equipped.
If you've got a Mode C Transponder Enconder the altimeter will get checked on a static basis, but depending on the day, might test OK at 29.92" but be flaky elsewhere; the Airspeed never gets checked.
If this doesn't show up anything, borrow a Magnahelic or Shortridge differential pressure meter from your Friendly Local Heating Ventilating and Air Conditioning technician, and compare readings between your pressure and static side of ASI and the other 'Cub. This can also be real handy in analysing engine cowling anomalies. (Used to have one of each in my engineering desk drawer until the layoff....).
Last chance, send A.S.I. out for check/repair to certified station. Rarely needed, in my experience.
Actually, a basic Magnahelic isn't that expensive from, e.g., Grainer's. Some of the glider guys have one one their panel hooked to a trailing-edge flap "wake rake" to measure Delta P between upper and lower tailing edge (lowest delta=best flap setting for a given condition....) But that's maybe more than you wanted know.
Hope this helps. Cubscout