I had installed the Opera Mini 5.1 browser on my LG GT550 (Encore) a few months ago. It worked great and offered a superb web browsing experience. Cool.
Problem: every single page load gave me a Java alert, noting the app being an untrusted midlet (an unsigned Java application) that was requesting network access. It's been frustrating to always confirm 'Yes' with each page load as I browse the web. Ugh.
Well, after searching around, I just discovered a solution to this annoying problem: When downloading (or in my case, re-downloading) the Opera Mini browser, I went to an "other downloads" section on their site and retrieved a better version of the browser. This 'other downloads' area was easily accessible from the main download page, and the alternate version is still Opera Mini v5.1 for my phone -- but it's the "All Certificates" version that apparently includes the necessary midlet signing.
Re-installing it was a snap; it even maintained my previous Opera Mini settings (after confirming with me), including my bookmarks. Nice!
Now, I only get 1 network-access alert at the beginning of my browsing session (but without the "untrusted midlet" mention), and after confirming, I'm no longer bothered by it on subsequent page loads. Cool.
Hopefully others with this same problem will find this thread and successfully employ this solution. I presume it may work on other phones/devices besides just LG.