I am using my iPhone application on my iPhone 3G OS 3.0.1 without any problems. The application connects to an API URL at https://api.serverdensity.com/1.0/ and all requests
I had the same problem!
Did you install there "Intermediate Certificate Bundle"? If you don't then you will get the untrusted server certificate on all mobile platforms (and some PC ones as well).
Web Site Quote:
Before you install your issued SSL certificate you must download and install our intermediate certificate bundle on your Web server. You may also download the bundle from the repository.
Check out the GoDaddy SSL install instructions for your web server setup.
The Intermediate Certificate Bundle can be found here.