Well you are using Ubuntu, try using a real Linux distro :p
Jokes aside, I just tried Brawl myself with my 360 controller without issue. Like I said, something's screwed up. Have you tried using the stable 4.0 release instead? Another thing to try if you could: click the Graphics icon and go to the Advanced tab. Under Misc., you should see an option called Show Input Display. It should show a little "P1" in the upper-lefthand corner now. Play Brawl and start moving buttons around. It should show you any input Dolphin is sending to the game. Does anything show up or does it show up but refuse to do anything in-game?
Jokes aside, I just tried Brawl myself with my 360 controller without issue. Like I said, something's screwed up. Have you tried using the stable 4.0 release instead? Another thing to try if you could: click the Graphics icon and go to the Advanced tab. Under Misc., you should see an option called Show Input Display. It should show a little "P1" in the upper-lefthand corner now. Play Brawl and start moving buttons around. It should show you any input Dolphin is sending to the game. Does anything show up or does it show up but refuse to do anything in-game?