At some point in the game, neutral "Faction Buildings" can be renovated for one of the three factions: Courtesans, Thieves, or Mercenaries. Other than getting quick access to that particular faction, is there any advantage or disadvantage inherent in this choice? Also, can I change my mind later?
Renovating faction buildings aren't too rewarding IMHO. Sure they give you income and make faction members available in the district, but in my personal experience, I never needed a faction's help except in the forced missions. There's no real disadvantage to it other than a loss of some coin (but that's a given) and you can only have a single faction in the district at a time. But then again, I don't feel you really need their help.
You can however always change factions after renovating for another. You'll just have to pay for the renovation again for the next faction.
It really matters in some missions as far as Brotherhood (or any other Ezio related series) but Drunken pirates in AC Black Flag are not that good and you are better off without them.
Thieves are really cool in both Brotherhood and Revelations for once their faction ability is unlocked they can collect money (Technically Steal) for you and they can avoid an entire conflict by luring away guards which could be very useful on certain places. Same applies for Mercenaries and Courtesans (romaines in Revelations) they can fight for you or hide you from guards respectively.