Utilization of extended dash dancing helps Falcon a lot, although it's not an intuitive movement option so it'll take a lot of practice to fully implement this. Still having a lot of trouble utilizing it in many scenarios where it would've been useful if I had it hardwired. The way it works is you input a single dash, then quickly tilt the controlstick in that same direction (1 frame), and then immediately dash the other way. Continue this as long as you want and change directions whenever. Does the same job as dashing and rolling back except considerably faster, safer and for the opponent much harder to react to.
Other than that, I'm gonna be really basic here for anyone who might read this. Use bair, nair and falling uair for zoning. Bair is safe on shield and upon hit at low to mid-low %s sends the opponent sliding and gives you a dash grab or dash attack follow-up. Uair is safe on shield vs taller characters since it allows you to space it as far as possible, and true combos into every aerial Falcon has at a huge range of %s. If your uair misses or gets shielded always follow with jabs or grab depending on your opponent's punishing habits. Hell, try crossup dair sometimes. If shielded it's relatively safe and if hit, that's usually 14% plus a follow-up.
Falcon can punish most projectiles in the game from mid range, you just have to react to it or read habits and powershield -> punish option (usually jab, grab, ftilt or dtilt) or dash grab them before they get the projectile out. For example Ness, Yoshi, Lucario and Villager to name a few can't use their projectiles safely against Falcon.
Dash attacks are for opponents who are throwing constant hitboxes out with sh aerials, dash grab for basically everything else including punishing. Falcon is easily among the best characters in the game at rushing people offstage with his sliding dash grab and true combo dthrow setups into nairs, uairs and even the knee if caught with a bad DI which isn't too unrealistic considering dash grab into dthrow in its entirety can be approximately a third of a second long of an event.
Then of course we've got empty hops into grabs if your opponent gets shield happy about your aerial approaches. Keep conditioning them to do that and when they get conditioned for grabs switch back.
Aside from zoning with bair, nair and uair, defensively you've got pretty much the most useful jab in the game, a decent shield grab contrary to popular belief and a yolo fsmash and side-b for pulling back and then striking with massive range.