It's taken me months to figure out how to turn my frustration into a specific cohesive feature request. The problems lead to fundamental interface dead-ends, but are hopefully not ridiculously hard to solve.
Using the app is a very one-way process. Any time you need to back up, you lose your place. The sidebar and tab bar are only visible on the highest level, and to get back to them, your "progress" is forgotten.
This is most important in search.
Rather than bringing up a modal search window, allow access to the tab bar and sidebar inside a search.
This was previously a larger question which was too broad. It has been fractured and scattered to the wind.
Previously part of this question:
Show realtime results while searching for tags in app
Switch to Questions tab on selection from Tags tab in app
Non-modal question dialog in app
Let me access the sidebar from asking in app
Restrict site specific views to specific tags (answer)