If you rush to use Twitter for Customer Service, you will fail.
Twitter is not integrated with enterprise applications.
The lack of out-of-the-box integration capabilities in Twitter mean it lacks the ability to transfer information in either direction. It does not capture the Twitter interaction record, as you would a chat interaction or email thread, and thus it cannot become part of the record.
Twitter does not allow you to build a deep customer experience.
If you deliver coherent customer experiences you need to provide a similar response to the same question across all channels. You can use SLAs to determine which channels will cover which interaction. Alas, the broad availability of Twitter means you cannot highlight to clients which interactions can and cannot be conducted over the channel. Nor can you control at which point in the process Twitter can be useful, as you would with chat or email by providing a link only at a specific time.
Twitter will force you to push customers to another channel to finish or continue an interaction, and destroy your seamless, integrated Customer Experience.
These problems can all be worked out through customized development and taking the time to think what you want to do, how you want to do it, and why you want to do it. It is all spelled out in your customer experience strategy.
You do want to use Twitter to enhance your Customer Experience – right?