Diddy, Rosalina and Ness actually don't pose that much threat to Falcon on a higher level. Falcon can break into Rosalina's zone quite easily and get rid of Luma instantly with rapid jab, and while offstage is extremely dangerous for Falcon in this matchup, it's pretty much the same for Rosalina. Falcon also juggles Rosalina as easily as she juggles him.
Diddy we are currently discussing in the matchup thread I made so I won't go into him.
Falcon beats Ness in neutral pretty definitively. Ness is slow and PK fire isn't safe to use against Falcon in mid range. Falcon just gets comboed by Ness harder than Ness does by him because Falcon doesn't really have much defensive options in the air whereas Ness has a 3 frame nair and his disjointed fair to get away from more situations. You just have to space your follow-ups properly and occasionally bait his aerials out and punish him for them. PK Thunder can be annoying but it disappears if you hit it with bair or uair which is easy to do, meanwhile Falcon outright destroys Ness offstage if Ness has to recover low (try to force him into that by punishing his offstage fairs from below or waiting them out and then bairing him).
I'm surprised to see people thinking ZSS is difficult for Falcon, as I find it to be a very even matchup. She can't safely try to grab Falcon and her approach options are very limited. As long as you don't get paralyzed you can eventually punish her footsies, combo her and KO her much earlier than she KOs you especially if you DI her up b every time (hold up and towards ZSS when you anticipate she'll do it).
Sheik and Pikachu are Falcon's worst matchups by far. Sheik outperforms Falcon in neutral, combos him harder than Falcon does her, and can recover very safely whereas you are in constant threat of being gimped. Your best bet is to force her to recover low and abuse the ledgesnap vulnerability on her recovery with bair (it's surprisingly easy as long as you avoid her up b startup hitbox), and in general try to KO her early because that's one field where she struggles especially in comparison to Falcon.
Pikachu is hard much for the same reasons except not as prominently, but he also has a tiny hurtbox that can avoid your jab and grab in a lot of his landing animations. These still aren't terrible MUs in my opinion, but currently I view them as Falcon's worst ones.
Sonic might be on the bad side, but I've yet to play enough versus him to say, and now that his bthrow got nerfed I'm not so sure. Just mentioning this to be as thorough as I can.
DK vs Falcon I think is pretty even (or slightly in Falcon's favor) since both characters strive from the fact that their opponent can't harass them with projectiles. It's a very aggressive matchup, and I like it a lot because of that. Falcon can use his speed to punish DK for a lot of things and combo DK so hard it feels kinda bad sometimes. DK's pressure is pretty good though. He can also easily gimp offstage Falcon by hanging on the ledge when Falcon is recovering and using his up b or bair at the right time to send him farther and farther back, but Falcon's dair is a serious threat to DK as well.
's Dair pretty much kills you everytime offstage. Its a long lasting, disjointed meteor that can take out Falcon's already unreliable recovery extremely well. Also, if Luma is next to her then you can be punished for getting a grab. I've grabbed Rosalina multiple times, immediately went for a Dthrow without a pummel, but I got hit by Luma's Nair/Jab or whatever. I don't know if its a guaranteed punish or if Rosalina buffered it/did it as I grabbed Luma, but against one of the few good Rosalina's I've faced I had to give up going for grabs because of that happening multiple times. 
