I had an experience where the 2nd controller in Virtual Console would only move, not jump. This happened with both the WiiMote and the Classic Controller.
To troubleshoot this problem, I deleted one of the virtual console games and re-downloaded it. Same problem. I verified that I had the latest system update, too.
The problem was resolved by unplugging the gamecube controllers from the Wii unit.
According to Nintendo support, having these connected can conflict with WiiMote controls.