Unplug Audio Cables
Similar to the Bluetooth bug above, Siri sometimes just doesn't work when you have headphones or an audio cable plugged in.
In the car I plug in my iPhone to my car's stereo using an audio cable, and whenever I do that, Siri doesn't work. It will activate, but it won't recognize anything I say.
Again, this is likely due to the possibility of Siri thinking that you have headphones plugged in that have an inline microphone that you can use for Siri, but if you don't, then Siri will be listening for commands through a microphone that doesn't exist.
With that said, it's best to unplug any audio cables from your iPhone if you want to use Siri, at least until Apple fixes this bug.