If you installed the update from the SSBB disc then you're fine. Do NOT install the latest Wii update from the internet!
Now if you don't mind playing in 50Hz just set your Wii to 50Hz in the settings and it should work, however, 50Hz sucks.
To play the game in 60 Hz mode just download the Detal Freeloader, keep your Wii at 60Hz and use the Freeloader to boot the US SSBB, with this you'll be able to play the game in 60Hz mode perfectly fine.
Just one thing, when you insert the freeloader in your Wii a blur like thing will go over the screen twice, that's normal, once the blur's done its job don't click start or anything, just eject the freeloader disc and then insert your SSBB disc, go to the game channel and hit start, there you have it working SSBB in 60Hz.