Does the gentleman not exist in this game or is it just me? The knockback from the first two jabs normally knocks the opponent too far away to use the gentleman, and even when it does connect it has virtually no knockback. I've never played any other smash game so is there some kind of trick to doing it or is it just not as useful in SSF2?

Just not useful, the knee hit has very little knockback.

Dang, that sucks :/

Falcon's hard countered by Kirby brahs.

Why so?

Also, Captain Falcon gets countered in a lot of ways nowadays (at least in online mode).

Have you seen how much Kirby recks him? Utilt all day man. It's like Smash 64 all over again. May not be a hard counter, but no Kirby should lose to CF.

Hey guys, would you mind watching this video and reviewing my captain falcon? I think I need to work on my edgeguarding, but can you guys point out some other flaws in my play? (I believe I played best in the first game of the set rather than the last.) Thanks.
https://www.youtube.com/watch?v=znsUeslFk7s#t=18m24s

Constructive criticism - I think you mainly need focus on techchasing, especially utilizing dtilt/ftilt out of approaches. A lot of your attacks are 1-2 strikes then you guys reset. You gotta try to link at least 3-7 moves together with falcon. For instance, at 19:25 you dash attack, then thats it. You could have dtiltx2 jabbed twice, ran in for a grab/or Utilt following it. Trying this combo right after missing your dash attack at 19:33 or 20:47 would have also prevented you from being punished because your dtilts would have out prioritized him. Other than that I am liking your accuracy on moves, keep it up.

Edit: Oh and SH nairs can be your bread and butter for getting past his projectiles and opening pika up!

Thanks for the tips! I'll try stringing more moves together.

If you don't mind, can you guys critique my falcon too? http://youtu.be/peulNNL-HCc I feel I did pretty good in this match.

At a glance, you do well on:
Connecting knees.
Using tilts effectively.
Not SDing.(Falcon is hard to control sometimes.)
Recovering well.

Work on:
Sprinting all of the time. The attacks at 1:08 looked very slow and awkward, as well as some other points in the match. A better opponent would easily shield these attacks. Sprinting allows for better combos too!
Using grabs more. You hardly used grabs at all in these matches. Falcon's dthrow, fthrow and uthrow all lead to almost guaranteed aerials, and are great for setting up combos.
USE AERIALS MORE! Falcon's aerial game is crazy good. Use shorthop nair to approach and space. Use dair to punish and techchase opponents on the ground. Use uair to combo.
Don't use sideB as much. Sure, throw it in once or twice a game for a mixup, but using it as an approach becomes very predictable and is easily punished.
Try to reduce lag if possible. Your game looks pretty slow, and while it might give more time for combos and reaction, it won't benifit you in the long run. Play on low settings and not fullscreen. If the lag was just from recording, that's understandable.
Use shield. Shield grabbing and generally reducing damage is very useful.

Overall you did well, just work on speeding up your play, and don't give your opponent time to react to your attacks (no more walking!). If I had to give one EASY tip, try approaching with shorthop nairs.

Playing on full screen is actually better, the game renders more easily or something. Resizing the screen can make the game lag, but as long as you use CTRL-F to full screen it is actually less resource-intensive.

Here is my short guide to falcon (doesn't necessarily apply to you, these are general Falcon things):
_Nair. Nair has high priority and low lag and a lot of hitstun, and it can be used to perform nair string. My favourite version of these is where you do repeated SHFF nairs, and you always get the second hit of the nair behind you, sending them back. Because you landed quickly, you have enough time to run and do another nair that sends them behind you. Rinse and repeat.
_Grab->dthrow/uthrow->knee or uair or nair or grab again, all depending on MU/KB/DI
_Uair is amazing. After nair, it is probably falcon's best move. I often find myself using this move more than knee because it is more versatile and just safer overall. It comes out super fast right at the front, learning to control the timing during a short hop can give many different followups (for example, an opponent lying on the ground can be hit by doing the latest possible uair during a short hop).
_His smashes are pretty useless lol
_His specials are, for the most part, pretty useless
_His tilts other than dtilt are pretty useless. They aren't the kind of moves you want to be throwing out in neutral. They are def more useful than his smashes though.
_Uair/Stomp->knee. These are the classic Falcon combos, and you need to be able to pull them off. Uair->knee is harder to do in this demo for many reasons, but it is still perfectly possible.

If I was to do a tier list for Falcon's moves, it would be...
S-Tier:

Blue Falcon, Nair, Uair, Dthrow

A-Tier:

Fair, Dair, Upthrow, Bair, Jab

B-Tier:

Dtilt, Fthrow, Ftilt, D-spec, S-spec, Utilt

C-tier:

Dash Attack, Getup attack, N-spec

D-Tier:

Fsmash, U-spec, Dsmash, Usmash

K-Tier:

Bthrow, Pummel, Ledge Attack, Jab2, Jab3, Jab3 loop

Jammy, the others critiqued you well, so I'll only add one thing: dash dance during the match, not just after a kill like 90% of people do online.

Thanks for the advice! I have a question though is there a preferred way to perform a SHFF on a keyboard consistently?

It's all about the timing, it's very easy to do. The tricky thing about Falcon's SHFF nair is if you do the FF too early you won't get the second hit of the nair.