I hit Escape all the time and often accidentally exit full-screen view as a result.
In other apps I can solve this by using Keyboard Maestro to remap Esc to command-., which will still cancel dialogs, etc, but not exit full screen. But in DTP3, command-. appears to exit full screen too. Is there any way of stopping that behaviour?
No, that’s not possible currently. Which full screen mode do you actually use - window or document?
Window
In which apps does this actually work? I tried Mail, TextEdit and Finder but in all of them both Escape and Cmd-. leave the full screen mode.
Safari 
I confess I haven’t done a large audit. I don’t use many apps in that mode.
Stop. Hitting. Escape.
Problem solved. 
I. Can’t.
I suspect that you need to hit escape for clearing the search field without needing to leave the keyboard and use the mouse to click the cross icon? 
If that’s the case, the only work around I know (and are using) is to drag the main window to full screen size instead of using the maximise button. Perhaps DT can consider to assign a short-cut to clear the search field.
Remapping Esc to Command-. also works to prevent accidental full-screen exits in BBEdit and Word, to pick two random examples.
Setting up a series of spaces can be time-consuming and it’s painful to accidentally break it by hitting a single commonly-used key. I don’t quite understand why Command-. ought on any view to exit full screen. I have no idea whether Apple has guidelines on that issue, and certainly don’t understand why Apple’s own apps don’t behave consistently.
and certainly don’t understand why Apple’s own apps don’t behave consistently.
Haha! Apple has been making rules then breaking them for years! 
True, but that is does not answer the question why
Haha! Touché
Fully agree that when I’m in search mode, by hitting escape I expect software to clear the search and get me back to the main browse mode (the way Finder works). For entering/exiting full screen Ctrl+Cmd+f is enough.
I have not found a way to change scope of search, clear search and go back to browsing by using keyboard. That’s why we cannot stop hitting escape, @BLUEFROG.
Navigation and search are the core functionalities of file the management app, they must be very accessible.
I’m very close to give up on DEVONThink and just go with combination of iCloud Drive/Dropbox for sync, Ranger/Alfred for file management/search and some editor (Sublime, Emacs) for markdown.
The next release will improve this.
Nice this is working now 
As I see this is working for the search field and when you are in renaming mode of a document.
Can this be implemented too for renaming items in the sidebar ?
The next release should improve this too.