From what I've watched, many people go for really unsafe and low reward options such as fsmashes at low percents and knee attempts out of down throws or just plain raw ones. Always go for uair or nair instead, the knee requires a setup or a frametrap in which case it does work very well. Many don't realize dthrow to knee only works if buffered from a dashgrab if you catch a bad DI (or none) on specific characters, including Sheik, ZSS, Rosalina, Fox, Diddy, Pikachu, Marth, Lucina, Robin and Little Mac for example. On most characters it's really precise or doesn't work at all, and in most scenarios your opponent is going to DI it so it's a bad option.
Uair to knee is very easy on taller characters like Sheik, ZSS, Palutena, anyone from FE, DK, Rosalina, Dedede, Bowser, Ganondorf, ROB etc and is safe on shield when spaced correctly. This is a really legit setup and DI doesn't help because Falcon's uair delivers just so much hitstun. Falcons should be fishing for this a lot more, generally at 50-70%.
Buffered fthrow out of a dashgrab is a good combo throw at low percents especially on floaty characters. You can follow-up with nair, uair and dash attack, and only one of these is enough to send the opponent offstage possibly ending their stock later with a dair.
Bair is really good for catching the 1 frame vulnerability on ledge grabs for characters you can't reliably edgeguard otherwise. You can either just drop off and bair, or drop off, fast fall, jump back on stage and bair in the process getting ready for further follow-ups if your opponent techs it.
On-stage RAR dair into anything, usually knee, is a worthy risk as well. Falcon's dair has relatively small landing lag and high shield pushback, and RAR lets you face your opponent after pulling it off allowing for a faster knee follow-up or jab frametrap in case it gets shielded, and makes it harder for your opponent to punish it because you end up behind them.
Oh and rising/buffered shorthop uair hits characters that are Marth's height or taller, similar to rising bair.
These are some things I wish I saw more.
Actually I think I just discovered all of Falcon's MUs. Tall characters: 6:4, short characters: 4:6.