Every Organization must develop a social marketing strategy that works for them.  Choosing the platforms and tools utilize should be based upon your own organizational objectives, resources and needs.  There is no cookie cutter plan that works for all organizations.  However, it is safe to assume that most organizations will attempt to utilize both Facebook and Twitter. 

Unfortunately, most organizations and individuals do not understand that different fan/friend/follower rules should be
 utilized when working with these platforms.  Facebook is a much more intimate platform than Twitter; on Facebook you want to choose your Profile friends carefully and utilize privacy setting options to control what you share.  On Facebook pages, most organizations will accept any followers, although it might be wise to monitor who is following (every organization has disgruntled former employees).  You should not however apply your more restrictive rules of Facebook to Twitter.  Twitter is a less intimate platform which has evolved away from Facebook's reach-oriented platform.  As such privacy issues are not as prevalent and followers are a necessity if you want your tweets heard.

Recently I warned one organization that I was assisting that they should either turn off their notifications or be prepared for an onslaught of new Twitter followers.  I had taken temporary charge of their Twitter account with 15 followers and within 1 day had increased their followers to more than 300.  Within 1 week, we were over 2,000 followers.  Now, the followers they had were a combination of industry-related followers, locally-based tweeters and general audience (including marketers). 

An individual with the organization asked me: Do you think we are becoming friends with the right people (alluding to a particular group of politically vocal individuals)? 

I replied: "Welcome to Twitter, if you want your voice heard, you better be prepared accept and follow back any follower.  It has evoleved into a form of saturation marketing; if you want to reach any audience then you must be prepared to actively grow the account."

On Twitter, there are no "wrong people", the only poor audience is one that never retweets, mentions, shares or reciprocates.  There is software which can assist with identifying and purging those individuals.