Um input delay I think. It's just making the games run slower for both players, it's not a problem with the display. If that's what you mean.
My Wii is not too far away from my router. I get 4 bars on my laptop while standing right next to it. I usually have matches with less-than-noticable lag with some of my friends, almost like they were offline. I didn't move my Wii or change anything about my router, and everything's suddenly laggier. =/
Would it possibly help to erase some replays and other data? I have a lot of those, and custom stages. I've tried resetting my router a couple times, and tried setting a static IP etc. but that didn't work either.
I could try moving my Wii to a TV closer to my router, but since it's always had a good connection where it is now I don't see how that could be the problem.
The lag started right when I got my wifi working again, if you go back a page to where I posted about not being able to connect at all. So it's been like this awhile.