Yes, being able to add an item by barcode even if there is no API integration with product names and the names would need to be added to your account database manually would be very useful.  This makes adding an item you already have easier, but also for the person (who may not be the person adding) shopping to scan an item and ensure that they picked up the right one.

When scanning an item at the store, if it is in your shopping list it could be automatically marked as bought.

More widgets would always be welcome.  I don't think active icons in the drawer are a supported android feature even in 4.4 (correct me if wrong) but I have seen widget icons with this kind of functionality for adding to home screens.

Better tablet feature support would be nice to have but honestly, I would not take my tablet on a shopping trip anyway even though it is a fairly small Nexus 7 2013.  Still, it should not be a major undertaking to at least provide a landscape view for those who have only a tablet and no phone if for no other reason other than for the fact that it is a bit confusing to run across an app this day in age that will not switch perspectives when a device is rotated.

It always seems to me, between my wife and I, that when a shared list is changed that it gets pushed to the other device immediately... I'm not sure what more explicit sync options would really add here?

Simply having stuff delay moving is not good enough IMO because if you're not paying attention (such as holding phone while shopping, and accidentally tapping with thumb while not looking) they will still move and you end up having to re-review the entire checked off list at the bottom every time anyway to try to ensure you didn't miss anything. 

I think that the bottom line solution here is to make the check-off much more deliberate which would mean:

1) Tap and hold OR
2) Double or Triple Tap
3) Swipe across

Make the method user selectable in order to account for different preferences, but I wrote into support to suggest any or all of the above and was pointed here.  It really is a major annoyance in an otherwise nice and simple app for synchronized lists.

Another nice to have feature might be to even allow the user to define a "side" or area of the screen which does not register touches on the UI... this dead zone could be used to "handle" the device securely with one hand while shopping without worrying about your thumb on the screen causing any kind of unwanted UI events.