discrete stuff that i think is either critical to playing falcon at top level right now or will be in the future. will be updated occasionally
instant uair
solves falcon's biggest problem which is the lack of an aerial that comes out instantaneously (while he is rising during his jump) while having decent knockback. good for poking against falco, sheik, marth, peach, falcon, and fox (very difficult to land on fox, though). good for extending combos. good for denying certain aerials (beats spacies nairs if you hit at a very specific angle/frame!)
doublejump nair
your best option for when they miss a tech on a platform and you aren't in position for a stomp (or, you aren't in position to follow up with anything after you stomp them). goes into a knee at mid-high % in this case
also really good to use after a shffl'd nair if they DI/SDI up. doublejump so that you're exactly horizontal to them and nair them again. this is better than uairing them, which most people think is falcon's only option if they're at that height that isn't as close to the ground as falcon's shorthop while still being slightly lower than his fullhop.
pivot grab
the best way to abuse falcon's ridiculously fast foxtrot (the initial burst a character makes upon dashing -- falcon's is the fastest in the game). great for dancing around them when you think they're going to whiff something that only hits in front of them. don't use this against fox or falco because shine is broken and will hit in back of them even when you correctly read that they're trying to hit what's in front of them. similarly, watch out for nairs/other aerials that have hitboxes on the character's back. i.e., pivot grabbing is better vs a sheik that tends to fair when she's suspended in the air rather than one who nairs.
kneegrabbing
a while ago M2K informed me that if you knee someone's shield as low to the ground as possible, Falcon has +2 frame advantage (with the L-cancel lag factored in). this means that your grab beats theirs if they try to shieldgrab you (which they will do a LOT given how shieldgrabable this looks). i haven't tested this much yet but i definitely will in the future
180 degree ledgehop wavelands/180 degree wavelands onto platforms
most characters safely ledgehop so that they're elevated a bit higher than the stage, then airdodge diagonally down to waveland. because of falcon's ball-shaped 2nd jump, its really easy to get the best waveland possible by airdodging 180 degrees horizontally. same goes for wavelanding onto platforms
spaced nairs/uairs vs crouchcancellers
CC'ing ***** falcon harder than any character because he has no fast moves that also have enough hitstun to give you frame advantage vs the CC'er. unless you hit them with a stomp or knee, they can hit you before you can combo them into anything. grabbing obviously beats CC'ing, but in falcon's case it is extremely obvious that he's going to grab if he dashes up to them because he has no other options to choose from. for these reasons i try to beat CC'ers by poking them with spaced nairs/uairs to make them leave their CC. stomp and knee are usually reacted to and punished in today's metagame which makes falcon's anti-CC game really weak. you shouldn't try to beat someone who's crouching; you should be giving them reasons to leave their crouch
juggling
with falcon you should seek to carry your opponent as [horizontally] far across the stage as you can during a combo. the reason a lot of people end their falcon combos prematurely is because they don't properly give themselves the frame advantage necessary to continue. what i mean is,
you should be hitting them with your aerials (usually uairs) as close to the ground as possible as to give yourself as much time as possible to hit them with another aerial. take landing uair -> uair -> knee on a fox at ~60% for example (assume he DI's in because this combo is impossible if he DI's out). after the first uair, you shorthop towards fox as fast as possible to land the second uair. the mistakes lots of falcons make at this point are A. uairing fox before they reach the peak of their jump and/or B. not fastfalling
these are both counterproductive to juggling because:
-if you don't fastfall, you have about 10 frames before falcon reaches the floor. this is far too long and the knee afterwards won't connect
-you cannot fastfall before the peak of your jump
the lesson to be learned is that you must uair during the 2nd half of your jump, and you must fastfall it/go into your next attack as fast as possible. falcon has TIGHT links that you can't otherwise land because of how fast people wiggle out these days. when i uair during combos, you hardly see falcon's legs come out sometimes because of how close to the ground i use them.
fall off the ledge -> bair/uair
falcon can fall off the ledge, bair or uair to edgeguard, then 2nd jump -> up-b and make it back to the ledge. good for edgeguarding people at certain positions below you, but you risk your stock in attempting it
example:
www.youtube.com/watch?v=rHkT8T-jJjo#t=01m43s
more to come