How can someone fix a stretched or compressed image?

With someone's face, I would use their eyes as a reference. Eyes/irises/pupils should be round. 

Unfortunately, once an image is destructively distorted, it will always contain artifacts (stretched or squished pixels).  You might be able to salvage the height/width ratio to some extent.  IMO, it's best to find a distortion-free image and use that instead.

In the new Photoshop versions, just don't hold down SHIFT when re-sizing your images. Aside from this, Photoshop allows you to accidentally or intentionally perform destructive modifications to your images. Photoshop generally doesn't know what you consider to be "stretched" or "distorted/compressed". It's something usually an artist looks at and understands that it is wrong. Other than a visual indication like "that circle is not a real circle" or "that square is not a square" or "that person appears stretched and distorted, it's all about using the tools correctly. As stated previously, in previous versions of Photoshop, when we entered FREE TRANSFORM (Command/Control+T) to re-size an image, maintaining the aspect ratio proportionally, we had to hold the SHIFT key down. In the current versions of Photoshop, this is not necessary. When re-sizing using something like FREE TRANSFORM, just grab a corner transform of your text, image or graphic object and drag. Photoshop won't let you change the aspect ratio accidentally or otherwise unless you now do the opposite and hold down the SHIFT key. Adobe is kind of building these features into their applications to prevent exactly what your talking about. If you have a single image open and you feel you have accidentally messed up the aspect ratio, it should be easy to see the issue around the edges of your image as the artboard should be the same size as your original. You can use REVERT to undo the changes you have made to the image. If you feel you have messed up the size or aspect ratio of your artboard, that is a different issue. That would be harder to detect unless you notice something visually. If someone has handed you a thousand photographs that you feel have incorrect aspect ratios, there is no AI that I know of that would auto-correct this. Maybe someone else knows of something like this. Anyways, if there is a more specific issue or question, happy to help! 🙂

What can you use to make sure your Photoshop images (or any image) aren't stretched and compressed? What standard or criteria can you use? What about some kind of reference image (that's proportional)? How can you tell that an image's aspect ratio is proportional along with the image? 

You pretty much have to eyeball it. size it till it looks good. Look for things in the image that might give you clues like round or square objects. Do you have a sample you can share?