One of the planes got stuck and I finally figured out how it happened. It requires some precise timing and hopefully can be reproduced with my savefiles:
load the dropship_launched.json it contains a dropship en route to the crashsight and an interceptor on way back to base
fast forward time (speed 2 or 3)
If it happens you will see the dropship reaching the crashsight slightly before the interceptor reaches his home-base. Then the dropship bounces back-and-fouth around the crashsight a bit. While this is happening, the interceptor symbol disappears from screen (like it landed). Then the ground mission starts to load.
Finish the ground mission (Just abort it for testing)
After return to geoscape and confirmation of mission result, the plane will be stuck
The plane is than on the same location as its base but it will not move. It is unclickable (nothing happens if plane, not base is clicked). On Plane Tab it will display the stats from before ground mission loaded (fuel is not empty).
So it looks like there actually happen some frames while Geoscape data is prepared for loading it back after ground mission. If one during these frames contains a transition from airborne to landed state, plane will be stuck in some in-between state.
It will only happen on the fast forward speeds 2 or 3 - it did not happen if I tried maximum speed. Since it may actually be nearly frame-perfect, I checked with fraps that the Geoscape was running with around 99 fps while it happened. While it is stuck, it was trunning at 150 fps (so it was calculating faster, probably no calculations for the stuck plane done). Furthermore here are my specs should they be needed for this: CPU: Intel Core 2Quad Q9400 @2.66 GHz, GC: NVidia GeForce GTX 570, 6 GB RAM - Game installed on a HDD, but windows on an SSD (so the Xenonauts savefiles are there).
Savefile after that: plane_stuck.json
Screenshot with the stuck plane (the squadron 2 on the North America Base):