I'm a pessimist at heart and first thing that comes to mind are military issues.
Which nation has the most powerful superheroes? They will replace the nuclear arsenal as the method of deterrent and in the case of single persons like Superman could tip the scale decisively on who gets to be a superpower or not.
I'd also think that military budgets would have sizeable chunks of it sunk into genetics and/or biotechnology research to be able to produce powers on demand.
Socially i think our world would be wrecked when the first Supervillains with global powers appear, i.e. powers that are way beyond a normal humans abilities or ability to counter such as Superman.
The first time someone like that would kill some civilians the world would explode in demands or regulation and/or "permanent solutions" like methods to remove superpowers or prison for life (real life sentences and not those you get out of after 25 years). People are on principle distrustful or more powerful people.. in our age that means those hulking bodybuilder types. Now imagine if this guy is normally built (maybe athletic) but who could throw you to the next city or fly through a mountain.
In that regard Marvel's Civil War was brilliant in bringing up these issues (whatever you think of the practical execution) in that it posed the question what would happen if Supervillains become a true danger to Average Joe (something all comics neglected when they let their Superheroes battle it out in densely populated areas).
On the more positive side i think those Heroes who use their powers responsibly could improve lives tremendously. Think of a person whose abilities it is to make plants grow.. he'd make a fortune working for a wood company or on a wider scope send him to the rainforest and let him re-forest the entire area over time.. he'd pretty much be able to set his own salary.
Then there are people like X-Men's Forge who instinctively can invent new technology or actively analyze existing ones.. he'd be set for life in any technology company improving their products at an astounding rate.