Off the top of my head:

• Memory footprint. Allocations that "rarely" fail on a desktop OS may fail on a mobile platform
• Battery impact - on a desktop app, it's common to have a thread polling, or a background task. On a mobile platform, activities like this can drain battery pretty quickly
• Desktop applications often assume reliable network access. Mobile platforms don't have consistent or reliable network access
• If you're using automation tools (or other tools) to help test your desktop applications, they likely won't work on a mobile OS. You'll need to look for alternate tools or mobile versions if these are critical to your testing.

I'm sure there are big areas I'm missing, but the community should take care of that.

Off the top of my head:

• Memory footprint. Allocations that "rarely" fail on a desktop OS may fail on a mobile platform
• Battery impact - on a desktop app, it's common to have a thread polling, or a background task. On a mobile platform, activities like this can drain battery pretty quickly
• Desktop applications often assume reliable network access. Mobile platforms don't have consistent or reliable network access
• If you're using automation tools (or other tools) to help test your desktop applications, they likely won't work on a mobile OS. You'll need to look for alternate tools or mobile versions if these are critical to your testing.
• Location awareness -- if the app uses GPS or Cell-based location information, you need a mechanism to test related cases -- no location info available; unexpected locations, etc.
• Screen sizes and orientations -- In addition to different screen resolutions (especially on Android) and phone vs. tablet testing, most mobile platforms can dynamically switch from "portrait" to "landscape" mode without warning.

I'm sure there are big areas I'm missing, but the community should take care of that.