Don't you already get health problems? That must be considered a drawback, no?
Though to be fair, I find it strange that when a leader fail to do anything about health issues the population remains calm. If there is prolonged periods of sickness (or simply the amount of health issues get out of hand), one would assume that someone would start complaining. Same thing if all forests in the area disappears.
About global warming, the way it was implemented in Civ4 was pretty pointless. Both from a gameplay and realism perspective. I think everyone'd agree on that. If it reappears in Civ5, I'd like it to be more a diplomatic issue, as that's how it's mostly affecting the world right now. I can see how you can make AI dislike nations that don't do their share of pollution cutbacks, but I'm not sure how it could affect MP.
Unless they get any really bright ideas, I'm guessing we'll only see this in realism mods.