iPad: Weak or fluctuating Wi-Fi signals
There have been reports through various news channels that Apple sold well over 300,000 iPads on the day of its launch, and as expected with such a large volume of devices there are a few reports of problems coming in. One of the most prominent ones is with the Wi-Fi connection where the signal strength will be weak or will fluctuate, and result in either notably slow downloads, or relatively slow downloads in comparison to other devices on the same network.
If your iPad is having connectivity issues such as this, there are several things you can try:
Power-cycle the router or modem
Sometimes the router's tables and settings need to be reloaded and refreshed when a new device is added to the network, so try fully turning off and unplugging your router for a few minutes to see if that helps in the handling of the iPad.
Change router protocols and bandwidths
Go to your router settings and try different combinations of wireless protocols to use. Many support options for b/g/n, just b/g, or just g/n, or each individual protocol by itself. Having multiple protocols open is better for ensuring compatibility, but not necessarily the most optimized setup. If your devices share support for one protocol, try just that one. Additionally, try changing the Wi-Fi channel and other signal settings.
Change the router authentication protocol
Sometimes incompatibilities between the implementation of a specific authentication protocol on a device and the router can cause network slowdowns. Try changing the method used for authentication, to see if that makes a difference. Most routers support at least WEP, WPA, and WPA2, but there may be others you can try as well. Keep in mind that changing this will require you to set up all other wireless devices again.
Broken or faulty iPad
Try the iPad at various Wi-Fi locations, and try resetting and restoring the iPad to see if you can get it to work properly in alternate settings. If you cannot, then one possibility might be a fault in the hardware. Bring the device to an Apple store and as with any new release they will be happy to test it and swap it out if necessary. Doing this helps their production line as well, so they encourage and welcome it.
Keep in mind that despite reports of problems, many people have mentioned that their iPads work just fine. Additionally, some people are showing faster network access with their iPads than with other devices on the same network. Nevertheless, the iPad is a brand new device and will have some bugs that Apple will tackle in OS updates. The current OS may just be more of a modification to the iPhone OS to support the iPad's features, and the more compatible OS may be the upcoming iPhone OS 4.0 release.
Apple has released some knowledgebase articles on the iPad's network connectivity, which may be of some use to people: