I use dictation a lot on my iPhone. I have big thumbs, and typing on the iPhone's keyboard ledas to myna rerrors. So occasionally, when I see the dictation button is dimmed, I get quite frustrated.
iMore recently posted an article about how to fix this issue.
Apparently, this occurs when memory on the iOS device gets too low; the solution is then to force-quit as many apps as possible. You do this by double-pressing the home button to show the application switcher, then tapping and holding an icon until they all wiggle. Tap on the "do not enter" buttons at the top-left of the icons to quit them. Press the home button again to close the application switcher.
Since I saw the above article last week, I haven't had the dimmed dictation button, so I haven't been able to test this. I'd been restarting my iPhone when this problem arose. If you've seen this problem, please post in the comments to say whether this solution works for you.
Mac OS X Hints
http://hints.macworld.com/article.php?story=20130528020523852