The Nintendo Wii really is a wonderful console for the casual gamer, and has some great features, but there are also some major flaws which detract from the enjoyment that users can have.
Graphics:
This is a pretty common complaint in relation to the Wii. It really wouldn't have taken much to have made better graphics for the system, but they console/game designers didn't put in the effort. Graphics are a major part of enjoying any game, as they make you feel more connected to the game, more involved. The graphics in most of the Wii games are absolutely terrible, such as Wii Sports or Wii Playground.
Inaccurate Controllers:
This is especially evident when playing racing games. It's rare, but can completely mess up a race, a competition, everything you've worked hard for. The controller generally works fine, but then as you drive, you steer one way and the controller turns the other way. Generally, it's a slight problem, like driving off the track, but in a game like Mario Kart Wii, it can result in steering into a wall or water, which can cost you entire competitions.
Power Button:
The positioning of the power button is simply baffling. The number of games where you need to hold the controller sideways, you're actually being encouraged to turn of the system. You are holding your left thumb near the arrow buttons, and it's just so simple to catch the power button and turn of the game. It's annoying at the best of time, but at the worst of times it can lead to the loss of hours of progress in a game. Infuriating? Yes.
Space Constraints:
As great as the Wii's motion sensitive system is, it's very annoying trying to play the Wii with more than just two people, even with just the controllers. You bump into each other, obstruct each other's movement and can even hurt each other when you try to move quickly. There really should have been a tad more research done into the negatives of the system before rolling it out.