Disney released an update the the MyDisneyExperience app, and it seems to have made some progress toward resolving my biggest issue with the app - difficulty navigating the menus.
For some reason, the MDE app has two sets of menus. One set is now tied to the bottom of the screen (you can open it up to full screen) and contains "Park Info & Entry," "My Plans," "My Photos," and "Spotlight."
The other menu is more of a Walt Disney World "contents" menu. It's locked at the very top of the app and contains "Wait Times," "Attractions," "Characters," "Dining," "Restrooms," "Entertainment," "Events," "Tours," "Photopass," "Guest Services," "Hotels," "Recreation," "Shops," and "Spa." This menu allows you to display a list or map of relevant locations, and each location has further information when you click through.
I just cannot intuitively grasp this dual-menu system. For example, this very past minute I was attempting to find park hours and was scrolling back and forth in the top menu, expecting to see "Parks" somewhere. Mostly, the top menu seems to be for things that have locations (except parks), but it also has an extensive list of items in "Guest Services" that aren't really location-based. "Wait Times" also seems more informational than locational.
Disney has taken steps to alleviate my suffering, though. The new design at least front-loads some of the most important information, rather than relegating it to a hamburger menu that I never seemed to notice when I needed it.
"Today's Showtimes" and "Park Hours" appear prominently. But for some reason, "Wait Times" does not, and you have to go to the top menu to find that. "Attractions" does have wait times included, so I'm not sure the reason for the separate "Wait Times" page. Could it be that "Attractions" includes things like the Beauty and the Beast Stage show? Nope. To find showtimes for that, you need to check "Entertainment" (not "Today's Showtimes"). You get the point.