Answer:

Not everything.

The form factor of an iPhone is great for portability, handling messages, and doing lists.

It is not great for viewing a half-dozen tables on a single dashboard screen, or viewing a grid of 6x12 (like a medication list for many of my patients with chronic disease).

Here is a little wireframe (made very quickly with BalsamiqMockup) that offers my preliminary thoughts.

I doubt that I'd want to document a visit that had a complicated story using the iPhone. Too much keyboard work.

I could document a simple sinus infection or UTI, assuming I could do it in 6-clicks, my de facto standard for documenting an acute illness.

What would a surgeon want? On rounds, a smart phone would be convenient for:

automatically receiving key lab results
looking up today's vitals, labs, and I&O
viewing the OR schedule
viewing a clinic schedule
signing dictated documents
viewing imaging reports

It won't be too long till many EMRs have "an app for that".