The question what makes a headshot good is much easier answered after determining what makes a professional headshot bad.
Headshots are an art form, and so it is difficult to give the artist standards to work with. Therefore, the following should only be taken as guidelines, not rules.
Too much light from below. Amateur photographers often light too harshly from below the subject because they think it looks good. The problem is that shadows define facial features, and if there is too much light, the photo will look unnatural and you won't be able to clearly see the headshot client's details on their face.
Bad makeup jobs. Bad makeup is worse than no makeup. Remember that Headshots much not look very glamourous because the actor typically won't look that made up on a particular day. The more natural, the better.
Jewelry and items on the face and head. If the client wears sunglasses or jewelry, they will be viewed as distractions and won't work for the headshot. Remember that you can't have anything in the shot except for clothes and face.
Too much shadow on the face. In addition to having too much light on the subjects face, you can also not have enough. Remember that if there are too many shadows, a casting director might think you were trying to hide something on the actors face. Therefore, you should only have enough shadows to sculpt the face, no more.
Blurry and technically not proficient photos. If a photo is blurry or too dark, it is unusable as a headshot. Remember that your technical details must be perfect if you want a truly professional headshot.
Bad framing. Bad framing can really take away from a headshot. If you give the client too much headroom or not enough and you chop off some of their head, it's not going to fly. Learn proper framing techniques and you'll be set!
Not enough body showing. If you are cropped too closely in towards the head, the shot won't be useable because a casting director wants to get some sense of your body type too. I always suggest shooting a bit wider than what you plan to use later so that you can crop in. Then if you decide you actually want a wider shot later, it's no problem!
Strange angles. Don't be too experimental in how you shoot the Headshots. The camera can be tilted slightly, buy not too much. The client shouldn't be shot from an extremely high or low angle because those angles tend to make the client look thinner or fatter than normal, and can really take away from the photo. Actors should look in their headshot just like they look in reality.
These are just a few of the many things that can make Headshots no good. Remember, if you avoid all of these problems, you'll be on your way to getting great Headshots all the time!