I just bought a Xperia PLAY running Android 2.3.3, and seems like the only way to use voice dial is through the Google Search app, which is capable of voice dialing, voice texting, etc., at least according to the YouTube demo. However, it looks like those services are only available in the U.S., according to the comments.
Poking around the services running in my phone, there's a "Voice Dial" app running (the icon is something like a phone mic), but it doesn't show in my installed apps and I don't know how to activate it... any ideas?
Here's an image of the Voice Dialer app icon.