I think that I may have found the solution... Here's a quick recap...
I upgraded to iOS 8.2 Saturday morning (March 14). I let Apple handle everything without intervention and once the upgrade was complete I happily went about my day -- but discovered mid afternoon this weird problem with dictation. After replying to your original post I was fiddling around with it a bit longer and observed that the problem was even worse than I suspected. What I found was that dictation was completely hung. No matter what app I tried, dictation was not indicating that it was even listening. (e.g. There was no motion on the voice-oscilloscope indicator.) So, I decided to just restart the phone -- this is the first restart since the original upgrade. Once it restarted I immediately checked dictation and it seemed to be working flawlessly. I played around with it for nearly an hour afterwards trying all kinds of apps and situations and it worked fine. (Now my only gripe is that when I use dictation to send a text message using Siri, she's a little too anxious to send the message!)
So -- I think that the problem may have been caused by some kind of post-upgrade process. So if you haven't restarted your phone since that time you might give that a try and see if it resolves your issue.
Cheers