Is it possible to take down enemy recon planes?
Beyond the accepted answer, it is possible to also shoot down enemy recon planes with the M1 Bazooka - 1 hit kill (and possibly other launchers, however no personal experience with these). Lead in is required.
Apparently, yes, it's possible to shoot down enemy recon planes. According to users in this thread, it's fairly easy to do with an LMG.
Look up into the sky and find the Recon Plane. Shoot at it. Get enough shots on it and it will go down.
It takes like 15 shots max with the LMGs to knock em out. And you get 150 points for doing so, that goes a long way towards streaks
I'm an LMG guy and that's what I've been doing. Big points.
I always knock them down, very easy with the M1 Garand. Others don't seem to bother lol