Photography has always been first and foremost, a person and their camera. With new technologies however, photographers are now expected to do more than just snap an image with perfect exposure and composition. Now, especially in digital photography, photographers are expected to be post production masters as well.
I'll admit it right now, I hate post processing. Mostly because I hate the hours I have to spend making images with absolutely zero flaws, but its also because I'm a bit of a purist. I believe that the real work of a photographer should come from preparation of the shot. Get your exposure right and set everything up before you press the shutter. Do that, and you shouldn't have to do much post processing, if any at all.
I'll concede that I am growing more comfortable with post processing. I shoot 99% of the time in RAW so you have to work with your images a bit once they're imported if you work with Adobe Products. I also do a decent amount of portrait work and I've had to learn how to subtlety adjust aspects of a person in Photoshop. Now I learn by reading books, so the the one that I picked up was Professional Portrait Retouching Techniques by Scott Kelby. The purpose of this book is to teach portrait photographers how to do quick retouches to get portraits where you want them. My favorite aspect of this book is, "If you spend more than 30 minutes on an image, you're probably doing too much." When I glanced at that line while in Barnes & Noble, I immediately went to the register and bought it.
I'm going to reveal two fixes because they are pretty common knowledge, but also to promote a fantastic book (I have NO affiliation with Scott Kelby, I just appreciate an excellent resource).
The two major things I modify or "fix" are stray hairs and blemishes. These are the non-creatives fixes and the most common ones. The greatest tools for these are the spot healing brush and the clone tool.
For blemishes, zits, etc the healing brush (shortcut press J, it's the 2nd of the tools) is your greatest resource.
There are two keys to the healing brush: 1) is to select skin that's very similar to the spot you're trying to fix (to select Mac: Option + click and PC: Alt + click) and 2) is to go in the direction of the skin. These two points are key to keeping the skin looking natural. I frequently reselect the spot I'm sampling from, it just makes things work better. Going in the direction of the skin is probably the most important because if you don't, it blurs the skin - you don't want this because you want to see the detail. Going in the direction of the skin helps the tool replicate and replace it better. Another tip is to try and keep the brush the same size as the spot you are trying to remove. Now the one problem with the healing brush is that it doesn't do well against edges. You'll get a really obnoxious, blurred gradient that doesn't fit. This is where the clone tool comes in (shortcut S).
I use a really soft brush, which means turning down the hardness so I have a fluffy edge. It makes transitions a bit more subtle. The clone tool works just like the healing brush; just select where you want to sample from and then apply the brush. The difference between the two brushes is that while the clone tool copies exactly what you sample, the healing brush does a bit of guess work and calculates a best fit AKA content aware. So having this knowledge helps to know when to use each brush.
Fixing hair is pretty similar to fixing blemishes on skin. Start with the healing brush and clean up the hair that is farthest away from the head. Work your way from the outside in. Again, pick a brush size that's about the same as the hair you are trying to remove. The clone tool can be used, but its more difficult if you have a busy or complicated background. Try to stick with the healing brush as much as possible. One important note: don't remove everything or else your subject will have hat hair. This isn't natural looking and you want to try and stay realistic for most portraits. So leave a few stray hairs here and there. Its less work for you!
So those are the two quick ways of cleaning up blemishes and hair. I hope you find this helpful and again, I highly recommend purchasing Scott Kelby's Professional Portrait Retouching Techniques if you want to get into portrait work and do your own quick retouching.