Why can't I add or edit contacts on my new iPhone 4?

On my new iPhone 4, I can add a new contact after talking to them (Add as new contact) but I cannot otherwise add new contacts, or edit existing ones.

It looks like a bug. Is there a way to work around it, or do I have to wait for Apple to fix their issue? The phone is not jailbroken.

You can use the Contacts application provided in the iPhone 4, and create/edit contacts in there.

What's preventing you from doing so?

The ability to add and edit contacts from the phone app is still available. I tested this just now on mine.

I had the exact same problem. Go to settings, then iCloud, go to the 'contacts' switch and set it to 'on' and it will fix your problem immediately.