• AutoUpdate Framework by mbhavi : You can now automatically update Brackets, without leaving the code editor.
• Add drag and drop to move items in FileTreeView by boopeshmahendran : You can now manipulate folder structure from within Brackets. Move a file/folder from one folder to another with a simple drag and drop.
• Enable opening of remote(http|https) files in Brackets by swmitra : You can now open a remotely hosted web-page from within Brackets. Use Ctrl/Cmd-Shift-O shortcut and supply a URL to quickly open the file and review the code within Brackets.

Full change logs: brackets and brackets-shell

• Fix for 13839: Crash on opening file with error "sharing violation". by nethip
• Fix #13099: Disallow user to create files/folder using relative path by sdalmeida
• Issue #11261: keep the search bar open by petetnt
• Linux native menus checked entries by pelatx
• Bringing in ImmutableJS 3.8.2 by vickramdhawal
• Add 'onHighlight' optional event callback mechanisfor better extensibility features in hint providers by swmitra
• Fix layout issue in submenu by boopeshmahendran
• Fix to avoid window location change confirmation dialog while running tests - onbeforeunload conditional registration by swmitra
• Fix full screen window issue in multiple montiors by sobisht
• Linux native menus lost shortcuts by pelatx
• AutoUpdate Feature Health Data Logging Changes by niteskum
• Adding Analytics logging for JSRefactor, Live Preview, Quick Edit and more features by sobisht
• Disable GPU for Ubuntu18.04 by gautam0217
• Build fixes for Ubuntu18.04 by gautam0217
• Fixing issue 14163, F&R replaces all content of file when replacing new line by navch
• Fix Issue 14149 - Fixes Dns rebinding attack in CEF by sabanaya
• Linux: Add a check for file exist when "Show in OS" is clicked by sobisht

TODO: any brackets-shell updates? which of the below messages are applicable?

• A new brackets-shell build is required for this sprint. Be sure to rerun grunt setup before building.
• Recommended: rebuild or reinstall an updated brackets-shell (no critical updates, but there are bugfixes).
• Rebuilding/updating brackets-shell is optional for this release.
• Rebuilding/updating brackets-shell is not required for this release.
• brackets-shell's Node dependencies have changed. Run npm install before rebuilding brackets-shell.
• Some submodules were updated this sprint. Run git submodule update to ensure your source tree is fully up to date.
• A submodule URL was changed this sprint. Run git submodule sync and then git submodule update --init --recursive to ensure your local source tree reflects the update.

For details on the bugs addressed, please refer to closed Release 1.13 bugs. Not all fixed bugs will be caught by this search query, however.