Well there are two main issues that arise. One is employees tweeting and posting on company time using company resources but I think the main issue that is emerging for employers is what employees are saying on social media: what they're tweeting or posting about the employer, about their colleagues or about clients or customers of the employer.
Some employees believe that, because they post or tweet something in their own time on their own computer and from their own account, for some reason it's got nothing to do with their employment and the employer has no right or capacity to deal with that. But that's simply not right in circumstances where what is being posted or tweeted is inconsistent with obligations that the employee owes to the employer or where it cuts across the legitimate interests of the employer.
What employers should do to mitigate those risks is to establish a social media policy. If you look through the unfair dismissal cases that have emerged from the Fair Work Commission on misuse of social media, a recurring theme is the importance of having a social media policy and establishing clear parameters or guidelines for proper use of social media.
Some employers though get this wrong and they try to do too much with their social media policy, so they conflate the rules about tweeting or posting officially on behalf of the employer and the rules for what an employee can do in their own time. Now obviously an employer is going to have far greater control over what an employee can do officially for and on behalf of the employer as opposed to their ability to restrict what an employee can do on their own time from their own computer from their own account.
So you need to really establish two sets of rules or guidelines. If you try to conflate the two it can lead to confusion and overreach where employers are trying to limit or proscribe conduct which they simply really don't have a right to do.