A good photographer has a tripod... and lenses and cameras (plural) and extra lighting equipment, an assistant, and lots and lots of backup equipment. I take at least three cameras in case one breaks, but it also allows me to have more than one lens available at a time. Once i asked a photographer at a wedding what would happen if i took his camera and broke it. How would he continue photographing the wedding. He said he couldn't. If he had backup equipment, he could have. The tripod thing is a must, because a photographer should able to pick the background, place the subject, modify the lighting, and take 2-3 images and go on to the next photograph. If a photographer says 'a tripod interfers with my freedom'... and they push down on the button to take 40-50 pictures of the one setting, then they are relying on random chance to happen and they 'happen' to capture it. Good photographers do not rely on random chance.
A good personality is also a good thing... just because they take great photos doesnt mean they take great photos the way you want. Talk to your photographer and ask what his strong points are. Do they like candids? formals? black and white? etc. Don't be afraid to ask what their weak points are. If you love their portfolio, but dont like the person, you won't like the wedding photos.
A photographers portfolio is pretty much their best work, but if its the best they've ever done, is that all they've done? Can they show you weddings from start to finish? Can they show you several weddings from start to finsish, and is the work consistantly good throughout? A good photographer's portfolio will be as strong as every photo they take. If someone says they will take 3000 images at a wedding, ask how many of those are good enough to put in the album? 10? A good photographer will take 500 photos at a wedding, and all 500 can be used in an album. Quality is much better than quantity.