OK, so here's some speculation that might be wide of the mark, but maybe not. I started thinking about Perry's dad, and it got me quite certain that he'll play a bigger part in the story at some point. Apart from Lena and Ian we haven't seen or heard much about any of the other characters' parents, and it wouldn't make much sense to include him in the story without any plan behind it.
Lena has also met him twice already, once in the restaurant and once in Ian and Perry's apartment, where Ian also was present. It was also hard to miss the fact that Lena wasn't fully dressed during the last meeting, even though I'm having a hard time seeing the Mayor as a sexual alternative for her. But the point of that scene was clearly to have Lena (and Ian) bump into him again, not that Eva desperately wanted a scene where someone comes to fix the heater.
In his role it's also very likely that he knows Seymour. According to his agenda page, the Mayor's affiliated with a left-leaning party, so they probably want more or less the complete opposite for the city. But his agenda continues to say that "due to the current and complicated economic situation, they have been falling short on their promised social policies". This is obviously just speculation, but that sounds like a desperate situation where he could end up being influenced by Seymour if he makes some shady "I'll make sure you'll get more money and get re-elected if you make sure I get what I want" offer. At least it seems very likely that Seymour would use his power to influence the Mayor if given the chance.
I think it's becoming apparent that one of the biggest moral choices in the game is whether to stand on Seymour's side or not. And I could see the Mayor being an important character if you choose the other side – maybe Ian, Lena and Emma could team up to help the Mayor in bringing him down? In the former scenario that extremely mild hint at something sexual between Lena and the Mayor could also come into play: Seymour could for example have Lena seduce the Mayor to get information, or to help convince him to do as he wants.