Well I have a 256k/64k broadband connection, I do not know if that is bad or not. But its enough to play Mario Kart Wii online, and other online games.
To be honest I do not know what I would call a bad connection, I guess dial up would be. I have seen people on Youtube play online Wii games with Dial Up just fine for some reason.
Maybe the races end early because I just DC myself, I am honestly not sure. At least the lag in this game does not physically lag your character lol, you can still race around the track with no lag even though it might not be real time.
I know what you mean though, its annoying when somebody behind you teleports in front of you because of lag.