Facebook's recent efforts to make money might appease investors but the moves are frustrating one famous user: former Star Trek actor and social media supernova George Takei.

Mr. Takei, who has more than two million fans on his Facebook page, took to the social network on Wednesday to complain about "promoted posts," a new feature Facebook launched in the wake of its bungled IPO that lets celebrities and brands pay to ensure that fans can see their status updates.

"I...