Here are some ways I'd use an iPhone app for OmniOutliner:

1. As a to-do list... so I'd like to be able to check things off, move items around, view multiple columns, have the text wrap around and resized so it fits on one screen. Indenting and unindenting would be important as would sorting.

2. View and edit plans for a project (like my wedding)... in this case, I want an easy way to navigate around the rows and columns (headers should stay visible, potentially locking columns would help)

3. As a place to store ideas, thoughts... here's where hiding and expanding hierarchies would be really useful.

Formatting is not so important, although it would be nice to be able to bold stuff. Attachment support is not critical for me. Having viewing capability without editing capability is not of much use to me. I might as well export as PDF and use a PDF viewer.

Syncing is crucial in that changes I make on the iPhone should automatically make it back to my original document. I would ideally like the syncing to happen when I click the "Sync" button in iTunes without having to go to another app even if I initially have to choose what files get synced.

Good luck!
Chris