Whoa! Wait a minute who ever said anything about solving overpopulation. I'm just saying that from a career perspective caregiver can be rewarding. Also, to really be a caregiver you are going to probably have to be married with your partner working, unless you want to be one of the government dependents but then why are you asking about jobs.
However, I do have some issues with your points.
Food scarcity is normally not caused by society not being able to produce enough food. Well maybe we can't produce a enough meat for everyone to eat like a fat American, but we could meet the current worlds total caloric needs with some work. However, due to war, oppression, terrible government, stupidity, and callously choosing to say screw the poor I want double Steak we make that hard.
Energy scarcity: We have tons of Uranium and Thorium. If we could get off our asses and actually use it to build useful things like Modern power plants instead of bombs we might be able to have a sensible energy agenda.
Pollution Levels: The modern world needs steel and steel is dirty. Unless you want to go back to a pre-steel world we are going to have to put up with some pollution for the foreseeable future. But with good management we can limit the pollution.
Disease Susceptibility: People get sick. Always have always will. Poor people get sick more than rich people due to malnutrition or improper hygiene. Things are still better now than they were though. Maybe we should raise the standard of living in the rest of the world some.
Psychological Disorder: Always existed, society just killed people with this because they were "Possessed by the devil" before the enlightenment. I am not for a return to that idea even if it puts stress on society.
Political unrest: Come on wars are as central to human activity as breathing. As long as humans exist there will be war or at least arguments over something. If you think otherwise have fun in your utopia fantasy land. I welcome getting proven wrong.
Overpopulation in the Western World: Most of the western world is in demographic decline. (I'm assuming this is a predominantly western audience being English language and all.) The US and EU only skirt by with immigrants. So clearly we are not prolific reproducers anymore. Now for the rest of the world, they may have to tone down the reproducing, but unless we want to use that war thing to stop them I'm not sure how we could. And I'm not sure I can support a government that would go to war against the breeders it sounds to Nazi like to me.
Though in the end I agree with you. If we keep growing our population we will eventually run out of resources to support that population. In the end the only real answer is to get off this rock and colonize space. But that's not really an answer to the problem. It's just kicking it down the road for a really long time. (Universal Entropy and what not) Any other form of forced population control will require some form of world government. Otherwise the countries that don't comply will just swallow you up in a few generations.