As I have described here a few times here, here and here, employees may make negative comments on Facebook about their job. So long as the employee is deemed to be discussing “terms and conditions” of employment with other employees, then yes, the employee can say things the employer would prefer not to hear. They may do so pursuant to the National Labor Relations Act which protects workers’ right to form or merely consider forming a union.
According to a San Antonio Express News report, there have been some 100 complaints filed with the National Labor Relations Board regarding Facebook comments about work. See news report. Employees do not win every case. I am sure the outcome often depends on the diligence of a particular NLRB investigator and whether the employee can show s/he shared these concerns with co-workers.
If the employee merely gripes to himself, the comment would not be protected by the NLRA. In one case, the employee complained about pay and poor quality of services provided by the employer. The NLRB found that with no indication that the employee discussed these problems with co-workers or that she tried to take these complaints to management, then her gripes were not protected by the NLRA. If the employee cannot show “concerted” activity, then the activity will not fall under the ambit of the NLRA.
Employers should note one comment by the NLRB’s general counsel: many company media policies are overbroad prohibiting any negative comment about the employer on social media. Such a policy conflicts with the NLRA and should be avoided.