My advice for Falcon is to learn some godly DI and then take him to FoD. Falcons actually fear Doc too, according to their board. We all should know how to gimp Falcon's recovery... but on the stage its a bit tougher. You have to play very carefully. Use pills only when Falcon isn't in a position to get to you before you can at LEAST put up your shield.
Nair kinda works... differently against Falcon. If he jumps at you, you just wanna jump right at him and try to nair before he can aerial. It sounds dumb (and you actually have to be smart about this, seeing as you can eat many a knee this way) but it works. Wall of bairs can also be effective as long as you don't make it predictable (once again, knees) and uairs work great at disrupting combos.
Try not to CC too much either, or you'll find yourself down a stock when you get knee'd and you slide right off the stage. Hmm... Pressure on Falcon is great but kinda hard to do. Fulljumping dairs -> bairs work great, and double jumping reverse fairs can be awesome too. Short WDs with utilts can mess up Falcon as well....
I unno how to be much more specific. Comboing Falcon really isn't a problem (you can chain usmashes and etc) but its that once you start to get combo'd it can be ridiculously tough to get out. If you are ANYWHERE near the edge try to keep your second jump for as long as possible.