Watch for the signs of being unbalanced!
Unbalanced? Ok, not you or the photographer, but the image. The images to the right are the same. One is cropped closer to the right, the other the left. The top image makes the dog look like he's running into a wall, the bottom is following where he is going. Although still not my ideal crop, this shows that the second image would be the better shot to puchase - the dog should be leading you where he is going - not just ending.
Composition can be a long and boring explanation. So rather than bore you to death, I will say, think balance! There are photography "rules" but they can be broken and still get a good photo. NOT all rules should be broken though.
Watch for negative space. If it is working the the photo and taking you someplace, it can work. But think of a headshot - when the top 1/2 is nothing but sky or space, it looks unbalanced and bad. Watch for your photographer to balance your images to look great. If it looks off to you - then it likely is!Check out image samples here.