Although the market for centralized secure messaging is currently being served adequately by the likes of Signal and Telegram, centralized messaging platforms inevitably leak metadata.
I don't want to belittle the work done by teams that have already started work on distributed messaging platforms like Tox and Matrix (and my own proof-of-concept, Toc [1]), but Mozilla is in a much better position to tackle the problem of decentralized, private messaging that also has great UX, and not just in terms of sheer resources:
1) They have (or at least had) a decentralized identity management platform in Persona.
2) They have a decentralized, zero-knowledge data sync platform in Firefox Sync.
3) They have a lot of influence in the web standards community that they can leverage to push a new federated messaging protocol to succeed XMPP.
This is the kind of work that I think Mozilla should be doing, because they can do it better than anyone else who's willing (i.e. not for-profit corporations, because they have very little to gain by building decentralized apps and federated protocols that have no lock-in whatsoever).
[1] http://toc.im/
Seeing how hostile most of the western governments are toward privacy on the internet, that's probably not the best long term strategy for Mozilla though. They could quickly find themselves labelled terrorist organisation ( by mistake ) and have their account frozen ( by mistake ) for a long period of time ( due process, can't rush those stuff )
Here is a recent article about it http://www.theguardian.com/technology/2015/mar/11/tor-should...
On top of that, I'd argue IM + video/audio chat that respects privacy is something that desperately needs better solutions.
I'd push software forward, and then innovate on protocols. Peer to peer might be the only way to achieve true privacy.