I'd also want to be able to merge one list with another as well as being able to copy items from one list to another - yes, you can select all and then copy, but that's an extra step.
The integration with Woolworths' online shopping worked reasonably well. You get the choice of ordering everything on the displayed list, or only those items that are ticked. The list is automatically uploaded to the mobile version of woolworthsonline.com.au.
An irritation with that site is that while you're required to pick a username when setting up the account, you can only login using your email address. For most of us, that's a lot more characters, and the less typing you do on a phone, the better. (Yes, you can have the site 'remember me', but I'm not comfortable with that for ecommerce applications.)
The next problem is that orders aren't necessarily filled by the store you nominated as yours (the app suggests the closest to your GPS location when you choose 'your' store), so it is possible that some items on your list will be rejected as unavailable. If you go back and modify your list, when you try Buy Online again, you're back at the login page seemingly regardless of how quickly you make the change. This might be a 'you're doing it the wrong way' problem, but surely you'd want to change the stored list in these circumstances?
I successfully placed an order (in the interests of full disclosure I'll point out that Woolworths provided a $25 voucher towards the cost), and it was filled accurately and delivered within the three-hour time window I nominated.
Page 3: Conclusions