Our user base uses primarily desktops and iPads for accessing Appian. One issue

Off the top of my head:
1) Performance will be worse in comparison to using the Appian application, particularly in bandwidth constrained environments.
2) I don't think Appian explicitly supports mobile safari.

Dan, this is very good feedback to our UX team. Some of the behavior is governed by the OS - we do not have control over it, but some can definitely be adjusted. I personally think that mobile Appian is simpler to use than web but it has decidedly an "app" feel, rather than a "webpage" one.
Some items I can think about in addition to what Nate already mentioned:
- The web interface is not optimized for touchscreens, the text of some links may be too small for some fingers.
- dropdown/checkbox/radio button selections are pretty difficult, not all mobile browsers have a smooth operation (as a proud owner of a Windows phone, I know this first hand)

Also, the mobile app allows the use of hardware features such as capturing a photo, video, or wet signature during your process.