| Quote #1
Mayor Peter Stockmann: "I must say it all sounds most mysterious. Is there something going on that I am to be kept in ignorance of? I should have imagined that I, as Chairman of the governing body of the Baths--" (1.101)
When the Doctor withholds information from his brother, he unwittingly threatens the Mayor's power. Though Dr. Stockmann doesn't think of it this way, the fact that he has information that his brother doesn't gives him an edge. At this point in the play, the Doctor doesn't have any desire for the sort of power his brother has, but still the Mayor perceives him as a direct threat.
| Quote #2
Aslaksen: "I have a certain influence in the town, a little bit of power, if I may be allowed to say so." (2.131)
Aslaksen's position as head of Householders' Association and the Temperance Society give him a certain amount of clout around town. His support could mean a lot for the Doctor's cause. When Aslaksen withdraws that support he turns the tide of public opinion against Doctor Stockmann.
| Quote #3
Hovstad: "The idol of Authority must be shattered in this town. This gross and inexcusable blunder about the water supply must be brought home to the mind of every municipal voter." (2.156)
Hovstad plans to use the water supply issue as a weapon against the ruling elite of the town. By doing so he would shatter the town's power structure. He would, in the process, gain a lot of power for himself. This gaining of personal power could very well be his real goal.