Twitter has made moves to make it easier to use the service for customer support. It has announced a new, and simpler way to start a Direct Message.
When a business offering customer support wants to take the conversation private, there's now a single click involved. A deep link can be added automatically to the tweet with a call to action button, allowing the Direct Message to be sent immediately.

Additionally, it has added a Customer Feedback feature for users to provide feedback after completion of the customer support.
"Starting today, all businesses Tweeting around the world can start adding Direct Message deep links to their Tweets. Customer Feedback will begin rolling out to select brands over the next few weeks."
Making customer service even better on Twitter