Apple has just released a Knowledge Base document detailing a number of potential fixes for one of the Wi-Fi and Bluetooth problems that have plagued iPod touch and iPhone handhelds. The article specifically addresses the inability to use Wi-Fi or Bluetooth due to not seeing the Bluetooth or Wi-Fi address on the device. This includes getting a Wi-Fi signal but not being able to access the Internet, not being able to pair a Bluetooth device, and having the Wi-Fi or Bluetooth icon grayed out.
Four solutions are proposed in a step-by-step manner. The solutions range from resetting the network settings to restoring the device back to a bare 3.0 install, which erases all data. No worries there, since you can always re-sync your device with the information on its host computer, assuming you have a current backup.
The fourth solution is a bit darker. Call Apple for service. If this doesn't do it, you are directed to a second article which talks about re-doing your network settings and turning the network settings off and then on again.
Neither article deals with the basic problems of speed and sporadic signal strength. Please let us know if these solutions do the trick for you.