Look for faces. While many times you may be photographing from the back of the room, focus on capturing faces of your subjects rather than backs.
Find the light. Always try and catch your subject in a well lit environment, and avoid photographing people when they're heavily backlit (like windows, open doors, etc.).
Watch the background. While this one can take some practice, it can pay off big. Watch for the background in your images and try to find clean and meaningful backdrops for your photos. If you're limited on options, try hiding clutter behind your subject.
Move around. Avoid photographing an entire event from one location Look around for interesting angles on your subject, and if you're able, look for interesting angles from above or below your normal point of view.
Watch exposure. If you're using a smartphone and the scene is too dark or too bright, many phones allow you to tap the screen to expose the photograph for the selected area. This could dramatically help if the subject is backlit or too bright. This will also ensure the subject is in focus.