We have received multiple reports from 3.0 firmware users on original iPhones who are NOT experiencing the problems described, and who do receive calls without difficulty with the push notification service turned on. Cory's original post is left as-is below; however, we no longer believe the issue is widespread or will affect most original iPhone users. Our apologies for any undue anxiety or confusion.
One of the most awaited features, push notifications, requires a constant data connection. While the iPhone 3G can handle data and voice simultaneously when using a 3G/HSDPA connection, on EDGE (the cellular data service that the original iPhone uses) you are unable to take calls and maintain a persistent data connection.
Some iPhone owners might consider this a slap in the face from Apple, while other iPhone users will just be glad that their phone now has notifications. Either way, the good thing is that the voice mail system uses a data connection, so you will still get your voicemails.
Push notifications could also end up being a flop for other iPhone users too. Due to the structure of the service, push notifications can get lost in transit, and pushes to the same app (possibly all pushes) kick older ones out of the push queue.