The frequently asked questions has more information. Some of the most common issues are described below for quick reference.
The most common cause for problems connecting from your Nintendo Wii to your Mac running Wii Transfer is that the built-in Mac OS X firewall is enabled. You can add Wii Transfer to the list of allowed applications in System Preferences → Security → Firewall, or disable the firewall temporarily to rule that out.
For 10.4 Tiger users, you will need to manually open up the Wii Transfer port number. Watch this screencast for a walk-through.
You also want to make sure the Wii and Mac are on the same local network. See Network Setup for more information.
The Nintendo Wii has very limited memory compared to a computer. You may receive an "out of memory" error when loading long music tracks, such as audio podcasts, or when watching picture slideshows with music.
When you see this error, first try restarting the Wii. If the song was an AAC file that must be converted, disabling the high quality audio preference in Wii Transfer may product a smaller file. If the error comes back again for that music track, the file is too large and will not play in Wii Transfer.
For picture slideshows, clear the background music. Slideshows without music do not have the same memory requirements and should play through regardless of number of images in the iPhoto album or event.
See the Miis on your Mac section for tips on how to copy Miis to your Mac and what might go wrong.