Firefox 44 will be released on January 26th. Here’s the list of changes that went into this version that can affect add-on compatibility. There is more information available in Firefox 44 for Developers, so you should also give it a look.

General

• Move DevTools code to /devtools top-level directory. This includes changing a number of paths that could affect themes and extensions. Notably, JS Modules related to the dev tools now all live under resource://devtools/.
• Opening the “View” > “Page Style” menu causes unsafe CPOW usage warnings. This change removes the global getAllStyleSheets function and introduces the similar (but not identical) getBrowserStyleSheets.
• Stop doing random work in sessionstore for localStorage changes. This splits the MozStorageChanged event into MozSessionStorageChanged and MozLocalStorageChanged.
• Stop supporting installation of Sherlock plugins from the web. Search provider add-ons should be implemented using OpenSearch.
• Allow about: pages to load remote content. This bug deprecates NewTabUrl.jsm, read this comment for details.

JavaScript

• Breaking changes in let and const. Firefox 44 finally brings the let and const implementation up to standard, which also means some backward-incompatible changes had to be implemented. Read the linked blog post for the details.
• Remove __noSuchMethod__. ES6 proxies are a suitable alternative for many use cases.

Theme

•  Simplify gIdentityHandler. This affects add-ons that depended on the level attribute of #urlbar, which is no longer used. This comment explains what you can do instead.
• Impose size restriction on extension icons. This prevents too large toolbar icons from deforming the toolbar.
• alert() steals focus from other tab. This introduces various changes to the tabbrowser binding which could break themes.
• Remove outset border from notification bars.

Signing

• Firefox 43 is currently enforcing add-on signing, with a preference to override it. Firefox 44 will remove the preference entirely, which means your add-on will need to be signed in order to run in release versions of Firefox. You can read about your options here.

Let me know in the comments if there’s anything missing or incorrect on these lists. If your add-on breaks on Firefox 44, I’d like to know.

The automatic compatibility validation and upgrade for add-ons on AMO will happen in the coming weeks, so keep an eye on your email if you have an add-on listed on our site with its compatibility set to Firefox 43.

https://blog.mozilla.org/addons/2015/12/29/compatibility-for-firefox-44/