How would one receive notifications, pushed from a central server, without a network connection to the central server?

This can be done (if all tasks are on your iDevice); it's a new iOS4 feature:

"Local notifications - Your app can now alert users of scheduled events and alarms in the background, no servers required."

From: http://developer.apple.com/technologies/ios/whats-new.html

PS: with "can be done" I mean "RTM could implement this"...

Wow. I wish more developers would implement this. While I have wifi at work, they firewall the port Apple uses for notifications, so I never receive any alerts there. This is a great feature, and I very much appreciate your bringing it to my attention. Here's hoping Bob can add this to the post-iPad list, as this would be great.

this would be nice

+1

Now that I am this much more dependent on the terrific iPad app, I am all the more excited about this idea.

+1

+1

+1

Please implent this. Especially with iOS5, the Reminders app has this ability and it's making me split up my tasks! I really want to keep RTM as my main todo-list program but I need notifications!

Pretty please?

I agree with this. Now I am starting to rely more and more on RTM to get things done, this feature would be very handy

Please implement this! I find this feature super-important!

Native iOS reminders in RTM would also solve another problem. Currently, if you travel to a different time zone, RTM reminders will be offset by the number of hours different from your home time zone.