The shield is the main concern, certainly, as anyone with regularly practice against a Falco will attest. But if you also practice regularly against a Captain Falcon, you'll see another major issue: lightness. He's very easy to kill. And while his recovery is good against people who aren't used to dealing with it, it also goes a set distance in only one direction, so good players are going to have no real trouble making recovering very difficult for you. Also, it's actually rather easy to shield-grab you, and then G&W tends to fall into lots of throw combos.
So basically what I'm getting at is, that most any character would be considered bad, who has no real hope of living past 90% (or 60, if you're fighting Falcon, especially on a smaller stage). Of course, G&W also has some very damaging tactics (u-tilt juggle on Falcon into d-air spike into the stage into more u-tilts is one of my favorites), but those are mostly on fastfallers, who also tend to be the high-tier characters, all of whom destroy G&W mercilessly.
I've had lots of experience with that. I'm a Sheik main, but G&W is my secondary, and I play him regularly against Fastliketree and Xelic and Chang-sta and Rayzorium here in Austin, and... it rarely goes well, we'll say.