There are many reasons why the "unable to read disc" occurs. It can be the incorrect handling of the DVD to not loading the game disc properly or it can be a sign that your DVD drive is faulty. Whatever your problem is, the great news about Wii troubleshooting the unable to read disc is it's not that difficult to fix.
Like all electronics, the Wii is prone to disc errors that can be very irritating. Even though Nintendo offers a factory warranty on any malfunctions or errors, it's common for the "unable to read disc" error to occur after the warranty expires. Knowing how to troubleshoot and fix this error will save you time and money and you'll have your Wii up and running the same day.
You want to make sure that the disc is loading properly. If your Wii is standing vertically, then make sure that the label of the disc is facing to the right. But if your Wii is laying horizontally, then the label of course should be facing upwards.
Now if the game is loading properly but the unable to read disc problem still pops up then you may need to inspect the game itself. Any scratches on the disc can pose a problem. You probably need to get a micro fiber cloth or something similar to it and wipe the disc clean. Make sure that you wipe the disc from the center outwards, never wipe in circular motions.
If you are still having problems then you probably need to purchasr a DVD lens cleaner and give your console a once over with that. You can easily purchase this for as little as $5.
There maybe a few common Wii troubleshooting problems with the "unable to read" disc, but these are the common solutions.