As a heavy Signal user, from where I sit I personally see the following clear needs:
-Better group support. Right now, to do a group in Signal you have to name the group, which makes it kind of a pain to create ad hoc quick groups. I'm forever naming them "John Sue Bill" or "Jane Roger Amanda". iMessage, by contrast, just automatically makes a group without a name. You get a thread for that group, so you can follow the discussion clearly, and you can leave the group, but it hides the nuts and bolts of the fact that a group has been formed. Also, Signal has no per-group notification settings, so if you're in a "noisy" group your only option is to turn off notifications universally (including one-on-one messages and other groups) or live with it. Lastly, you cannot form a group from Signal Desktop.
-Better support for long messages (or a new product using the same network and security). Signal was clearly designed for short session lengths — brief messages that are composed quickly. But as it has become the catch-all app for encrypted comms — "just use Signal! PGP email sucks!" — many people, at least that I deal with, are trying to use it for email-type purposes. Long messages with arbitrary attachments. It would be nice if, like, putting a line break in a long message didn't mean hitting Control-Enter or Command-Enter. It might even be nice if you could have multiple threads with the same recipient. You know, like email. I am not holding my breath on this one. But if people could email as securely as they chat, using Signal protocol, it would be a huge leap forward in keeping the NSA out of our business. Not to mention Google/Gmail's ad clients etc.
-Ability to search. I can't full-text search my messages, even within Signal. As I use it more and more, this is a hindrance.
-Group video chat. This is very pie in the sky. But a lot of sensitive comms involve groups — think of people organizing a protest, or a corporate takeover, etc. And right now there are few private options.