Heh, I didnt know Falcon gave up so easily. I know whats bugging you, the grabs, the Thunder spikes, the DSmash...
I lost a semi final match against a really good Pikachu =/
But after I befriended him, I learned a little mind game that worked for me,
After moving in and out of his range, make him exaust his moves, and then go in for a grab, rapid punch, or a Sliding FSmash (whatever gets your momentum going)
As for his other B moves like BForward or his so called "Instant Transmition" (BUp), you can easily grab after these moves by spacing yourself enough so that his lag time kicks in after those moves.
I hope this helped in anyway, and dont forget to keep moving and play midgames