I'm not a Razr HD owner, but my anecdotal experiments yeilded decent photos, and the shutter seemed pretty snappy. It's certainly not the best camera on the market, but it's also not the worst. For a top of the line phone the camera doesn't quite match the best from Samsung and HTC (I have no experience with Sony or LG smartphones but some of their cameras get good ratings) however, the Razr will definitely outperform the cameras on most lower end budget smartphones, and it will blow flip phone cameras out of the water.
In low light situations it might be helpful to try and get the flash going, and you can always download a third party camera app to squeeze more oompf out of your smartphone, but unless your dad is a shutterbug I doubt he'll notice really negative problems with the phone. But if camera is your number one priority the Droid DNA is set to be out on the 21st of this month and it has the superb camera of the One X on it. So you may want to check the other options as well. But ultimately I'm a fan of Motorola hardware and I feel they make great phones. And even though the camera may not kill the iPhone, the Galaxy S3, or the One X (DNA), it's still a better camera then what you had two years ago.
I do wish that Motorola would sep up their game on the camera, and then it would be no contest which phone to buy, but overall the camera passes.