There are many elements that need to come together for a quality group photo.
1. Ensure proper focus. Getting proper focus is KNOWING how to focus first! Use one shot, target a hard contrast line. I like to use the line between the groom's lapel and white shirt. In many cases, if I have a few seconds I use live view and manually focus.
2. DOF. Get enough DOF to get the look you want. For family and "line-em-up" photos, you want everybody within the DOF. For more artistic bridal party photos, there are no rules for it. Put them all in the DOF or purposely leave people out of it.
All in the DOF:
DOF intentionally too small:
3. Exposure. Getting a good exposure is paramount to getting the cleanest and most detailed image possible regardless if it's available light or flash. Keeping ambient background exposures controlled also can help in improving contrast and detail on your subjects. Too bright of a background will wash out details of your subjects and can make them look "soft" and lose edge and outline definition.
For this pic, if I made the background brighter, we would have totally lost all definition in the hair, not to mention the smoke would be overcooked and it would blend into a soupy mess with the background. The good exposure on the faces provides a great level of contrast, detail and crispness.
3. QUALITY light. Getting high quality light on your subjects is very important. Hate to be the bearer of bad news, but contrary to what most beginner photographers say, overcast cloudy days are horrible for light quality. You get super bright foreheads and noses but eyes that are dark as hell. You can overcook the skin to see the eyes but the overall quality of the light isn't great. Getting good light throughout the faces will improve the perceived "sharpness" of the photograph.
Quality available light:
Inadequate available light:
The poor natural light can be improved with some flash.
Not only can you now see their eyes, it allows you to dial down the ambient exposure which brings the background to life too! The fountain is clearer, the sky is visible, the trees are more crisp, and it greatly improves the separation between the background and the subjects. They wanted the fountain visible in the background so it makes no sense to drown it out with poor exposure control.
Those are the very basics of getting quality group shots.