Tried it for the first time last night at Satu'li Canteen at Pandora. We were waiting in line for the river boat ride, so with 80 minutes of time on my hands, I decided to give the mobile ordering a try since we planned on eating after the ride. Ordering on the app was super easy, but I was afraid if I completed the purchase, I would have paid for food that would be sitting there waiting for me to pick up. I placed my order immediately after I got off the ride and what I learned was there's a button that says something like "I'm here, begin processing my order." When we got to the restaurant, I followed the signs to the mobile ordering pickup window and lo and behold, there was my order waiting for me! It was pretty slick! The only downsides were I had trouble changing the credit card linked to the app (I didn't want to use the particular card I had on file, and each time I tried to change it, I would get an error, so I ended up just using the card on file), but I think that was a one-time fluke. The other downside was the rest of my group opted not to try mobile ordering, so since I got my food so quick and they had to wait in line to order theirs, I ended up waiting a good while waiting for them to catch up.
In the app, if you click on your account avatar (mine is Donald Duck), you should see under the My Plans section a button that reads "order food." Pretty nifty!!!