1. Would it come across in a negative light if we tried to thank each customer by finding them on Twitter and writing a public tweet thanking them for using our product?
2. Other ways to utilize your existing customers to grow your business in social media?
Entirely subjective opinion, but I would think the possibility of this backfiring into a negative thing is too great. While many love to share every intimate detail of their lives via social networking (yuk!), that is their decision to do so.
Taken to its extreme, would you like a premature baldness company publicly thanking you for using their product? Doubt you would. And besides the pitchfork response the privacy advocates would launch damning your company, there is the legal ramifications of not obtaining permission to "use/mention" them in a company message.
Publicly thanking customers might be a bit much, as well as being pretty boring content. But more generally engaging with your customers on twitter is a great way to earn reciprocal engagement.
Celebrating their wins with them, retweeting their content, keeping an eye out for questions they ask that you can answer are all better ways to engage them on twitter, get them following you, and earn goodwill (and customer loyalty) that can turn into retweets and referrals.