Hey, cmalkiel! Not much point in sending messages if you can't see the replies! :/ Have you been able to get to the bottom of this? Do you have iMessage disabled on the phone and the iPad (we know that can cause some trouble with message continuity)?
Thanks for your reply. I've turned off iMessage on both my iPhone and iPad, and can (eventually) see SMS messages in the Digits app on my iPad, but I am not receiving any notifications that a message has arrived. I have to open the Digits app to see if a message was received.
I have all the 'Notifications' turned on in the Digits setting on the iPad, including persistent alerts, but nothing appears and I don't get any sound alerts. I have to listen for my iPhone to sound an alert, then look on the iPad to find a new message and reply... kind of a waste of time.
I might as well just use the iPhone for all my SMS if Digits doesn't work on the iPad.
I made sure that iMessage was turned off, and I'm now able to send and receive SMS
Some issues remain with the app itself, like being unable to switch between different conversations, but I'll search for that.