DNS propagation issues - Error 220602
Change your Wifi router to channel 1 or 11, Move your Wii nearer to your Wifi router or Change your DNS servers - swap the secondary and primary one round - this may fix it.
source
Check your router's broadcast settings to find out if it is set to "G", "B", or "Mixed." Mixed typically works best, but try all three to see if it improves the network connection to the Wii console.
Make sure that any other interfering devices, such as microwaves and cordless phones, are turned off. Wireless keyboards and mice may also cause interference.
Solution 2 (thanks Francis)
Wii User Agreement Problem (220602 Error)
1.) Go to Start/Run/Cmd
2.) type in \"ipconfig/all\" and enter
3.) Look for DNS ip adresses (DNS Servers)
4.) Write them all down
5.) 1st ip (Primary), 2nd ip (Secondary)
1.) Go to Wii settings, Internet settings, then Connection settings
2.) Click on your working connection
3.) Then go to change settings
4.) Go to the DNS settings and choose NO and then click ADVANCED
5.) Switch the ip adresses around. Put 2nd ip in PRIMARY and 1st in SECONDARY (PRIMARY (2nd ip) SECONDARY (1st ip))
6.) Click Save and Confirm