Her goal is to create a "utopia" by using ADAM and mind control to imbue everyone with the entire sum of the knowledge of Rapture's inhabitants, eliminate their free will and instruct them to act only for "the greater good" (turning everyone into mindless slaves).
Brain with a Manual Control: Mayor Phlegmming uses the manual override on Frank's speech control to instruct Frank to say that he'll take a cold pill for his initial symptoms, rather than seeing a physician as he'd intended.
In the first game, he was the typical Mission Control guy, who did little more than allow Sly to view previous cutscenes and instruct him on the different tutorials, occasionally providing comic relief.