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Try rebooting your iPad. Hold down the button on the top until the power-off slider appears. Use it. When the device shuts down, hold the button for a few seconds, until you get the Apple emblem. Launch OmniFocus once again and see if it works.

I believe the asking for the OmniFocus Sync Service password is a bug, and if you type in the password you set up for your Bonjour sync on the Mac, the right thing will happen.