If you have problems with the online check-in in the App chances are you will also have issues making dining reservations in the App Here's my work around although it doesn't make it any less annoying.
I hit the + sign in the app, then hit "Check dining availability", it spins like it's doing its thing and then kicks me back to the home screen, I hit the + then hit "Check dining availability", it spins like it's doing its thing and then kicks me back to the home screen. I play this game anywhere from 3-5 times and then the App goes through the prompts to send me a code, I input the code and then I can make dining reservation and check-in online.
I've been doing this for about 8 months ever since one of their illustrious App updates.
YMMV