For aircraft with variable-sweep wings, how unstable is it to have each wing in a different position?
This was an intentional test run by Grumman in response to US Navy concerns about asymmetric wing sweep.

From The story of F-14A, Aircraft No. 3, BuNo. 157982 


  One of these [flight tests] was in response to concerns raised by the US Navy regarding asymmetrical wing sweep. No. 3 is best remembered for photo shown at right. A series of flight tests were conducted from December 19, 1985 to February 28, 1986. Grumman's Chief Test Pilot, Chuck Sewell, conducted several trials with the right wing locked in the forward position of 20 degrees, and positioned the left wing at 35, 50, 60 and 68 degrees of sweep in flight. 60 degrees was determined as the maximum for landing. In the event of an operational in-flight malfunction, Sewell found the aircraft to be acceptable for carrier landings in this configuration.


Evidently it was manageable, and safe enough that carrier landings were permitted with asymmetric sweep.  There's no control available for the pilot of the Tomcat to intentionally asymmetrically-sweep the wings in flight, though.

How the handling qualities change I haven't seen reported anywhere.  I agree with Robert DiGiovanni that you'd expect additional drag on the side with the extended wing, but the Tomcat has additional options on how to move spoilers and other control surfaces and it isn't clear to me if it can detect and respond to asymmetric sweep or if it's just up to the pilot to do so.