Legitimate complaints are equally legitimate whether written, emailed, or twittered, just as malicious complaints are equally malicious however used. For some reason there are some red herrings being deployed in this thread to suggest otherwise.
There's a bit of an art to complaining, as you can get quite different teams with different powers replying to different communication channels - as others have said, sometimes forums can be the best method, sometimes letters, and sometimes twitter or email. Insisting on letters (or whatever) as The One True Way is short-sighted.
The only consideration is that a tweet is potentially public, and so may not be appropriate if you need to name a staff member. More importantly, if a situation requires you to name a staff member, I'd imagine it requires more than 140 characters worth of commentary!
Spot on! Couldn't have put it better myself.
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And how many TOCs do you think just follow people on Tiwtter? If they dont follow you you cant send a DM.
Not strictly true. Verified 'blue tick' accounts have the facility (or option, should I say) to allow anyone to DM.
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If you're managing a corporate Twitter account and have an iota of competence, then you'll autofollow-back everyone who follows you.
Autofollowing back is a little bit taboo in the Twitterverse for a number of reasons - firstly, it's insincere to simply auto-followback. Secondly, seasoned Twitter users will see "28,345 followers, 28,965 following" on a profile as an instant marker of a spam account or a sign of insecurity:
http://www.guardian.co.uk/politics/2012/sep/07/grant-shapps-twitter-followers-analysis
http://buyfollowerstwitter.co.uk/