If you are getting a 5 digit error code, you are unable to connect to the Shop Channel, or your downloads are extremely slow you are most likely experiencing interference.
Just like any device connecting wirelessly, lots of things can impact the network. We have found that if several access points (SSIDs) showed up when you searched for an access point, it is likely that they are contributing to the interference. Change the wireless channel on your router to avoid this interference. By default, most routers broadcast on channel 6, so try a less frequently used channel such as 1 or 11.
Also, make sure no microwaves, cell phones, cordless phones, or other wireless devices like a wireless keyboard or mouse are operating nearby when downloading.
If your system update is taking over 20 minutes, turn the power off, change the channel on your router, then test the connection again and start the download over.
This is a repost of NOA_ZACH's topic, I hope to edit it with even more oodels of information to help those with these problems, but for now I will be using a repost of his. If you wish to view the original page you may see it here:
http://web.archive.org/web/20070711140929/forums.nintendo.com/nintendo/board/message?board.id=internet&message.id=3153 (http://web.archive.org/web/20070711140929/forums.nintendo.com/nintendo/board/message?board.id=internet&message.id=3153)
If you wish to contribute something just PM me or post here 8).