On a low budget music video, my main concentration lately, there is rarely an art director / production designer / set dresser. Some directors come from a theater background or a crafty background and are very hands-on when it comes to dressing a set. Other are not, and it pretty much falls on the DP's shoulders to make it work.
I think as a DP the most important thing you can do is figure out what you see in the frame and what you don't see in the frame. Once you have that figured out you can re-arrange furniture, paint walls, light, and place actors to make the space feel appropriate for the scene/shot.
A common mistake seen on low budget / inexperienced sets is spending time on fixing something that is out of focus, barely in frame, or not in frame at all. This included set dressing too high above talents head with out low angle shots, stuff outside windows that aren't lit, things on the floor with no wide or high angle shots, etc.
I'm looking forward to the day that I can have a meeting with the set designer and plot and design all of the practicals on the wall/set and pick the color/tone of the walls to match the over all art direction.
I'd say the next important thing to do as a DP/Art Director is to light the good and stuff and flag the light off the bad stuff. Bad stuff can include talent.