I'm an other...
I can connect and surf the net on my home Wifi network but I can not "find my iPad". It is listed as "not on a data network". Two iPhones, an iMac, and an iBook all logon on fine. In addition, if I put a contact or calendar event on the iPad it does not push to the iMac or iPhone. If I put a contact or event on the iPhone or iMac it will push to the iPad. If I reset the iPad, the contact/event will push from the iPad to other devices. Nothing pushes to the iPad on home Wifi (AP alerts, ESPN game scores, or Facebook updates). I have a Verizon DSL modem with a built in wireless router. I have updated the firmware and no improvement. I too have had an issue with logging on to free Wifi for registered guests at a hotel. I figured there was some sort of Flash element in the login splash page. It was very frustrating and the IT guy at the resort was off for the weekend so he could not trouble shoot the login issue.
The thought had occurred to me to return it for another one but I got it on launch day back in April.