If you attempt to check or uncheck items in the Shopping List when offline, it does not sync back up when you’re online again.
For example, if I pull up the Shopping List in the HA app on my phone before I go into the store and then lose connection in the store, the list isn’t very usable. You can check items on the list, but they don’t move to the completed section. And when you get a signal again, anything that was checked becomes unchecked again. So if you get a signal halfway through your shopping, your list reverts. Or if you don’t get signal until you’re done, you have to go back later and check everything again.