Visual Voicemail
It would great to see this feature available. It's built into the AOSP dialer and there's another implementation here.

I second this. Other features it's missing and that AOSP have are Helplines, TTS accessibility setting (I personally don't find this feature useful, but adding it could potentially widen Simple Dialer's user base), My info button and an easy way to share it provides (technically part of Contacts app, but relevant since Dialer and Contacts are closely related apps), Emergency info shortcut (again, technically part of Contacts), and Contacts account syncing, including through DAVx5 (once again Contacts app).
Voicing support for this feature as well. Lack of visual voicemail is the only think holding me back from switching over to Dialer.