i am having the same problem, mixed mode works just fine, but wireless g doesn't work alone. I would think the Wii is wireless b only, but on the Nintendo customer support pages they seem to imply the Wii has 802.11g too.
Check number 4
http://www.nintendo.com/consumer/systems/wii/en_na/onlineWirelessSlow.jsp
Check number 4
http://www.nintendo.com/consumer/systems/wii/en_na/onlineWirelessSlow.jsp