Basically, Falco has two things going for him. Lasers, and the chain grab. The lasers can be avoided/perfect shielded by a good player. People are learning to get out of Falco's grab setups, too. He doesn't have the best range up close, and the grabs only work until 40 or so percent anyway. With the advent of teching the spike, it removes a lot of the danger and it becomes damage instead of the stock. Still dangerous and it's a lot of damage, but not catastrophic.
What with Falco's trouble killing, there are a lot of characters who can eat the chain grab damage and still be closer to killing Falco than he is to killing them.
He's got a strong ground game when he's right up close, but lacks range and will lose on the ground to quite a few characters. His air game is decent, but not enough to get by on.
Myself and Melee1 both agree that he has bad matchups with MK, Snake, GW, ROB, Ice Climbers, Wolf, Fox, Marth, Wario, and Kirby. I haven't actually discussed these matchups with D4ba or Sethlon, but I bet they would agree with me on a lot of them. That's a lot of bad matchups against popular high tier characters.