I just booked our fastpasses two days ago and we got all the attractions on the day we wanted and I really only have one time that was off from what I wanted. We found it all went pretty smoothly. With our hotel ressies we are technically a 9 day trip, hitting the parks day 2 - 8.

Most limited availability was Slinky Dog however we found plenty of morning slots for Slink by going to day 6 of our trip. Flight of passage was readily available for days 5 and 7. The only one I had to change the time I really wanted was 7 Dwarves, which was the 4th fast pass I attempted to book on the 2nd day of our trip.

As others mentioned pushing more desired fast passes to later in a trip makes it easier. Also don't book all three fastpasses just because you are working on that day. i.e. I booked slinky dog for day 6 but circled back to book my other two fast passes for that day after getting through flight of passage and 7 dwarves on other days.

I also booked via the app and had no issues. I much prefer a nice touch screen to a mouse.