The "broken windows" theory comes from a 1982 Atlantic Monthly article on strategies to reduce vandalism.
Consider a building with a few broken windows. If the windows are not repaired, the tendency is for vandals to break a few more windows. Eventually, they may even break into the building, and if it's unoccupied, perhaps become squatters or light fires inside.
Or consider a sidewalk. Some litter accumulates. Soon, more litter accumulates. Eventually, people even start leaving bags of trash from take-out restaurants there or breaking into cars.
My theme for January (and possibly February as well) is to fix broken windows (or as GTD puts it, open loops). That is, to clean up all the half-finished miscellanea in my life. This ranges across everything from finishing books I've started to cleaning out that last box from my move six months ago to ongoing things such as not letting dishes, garbage, and laundry pile up for too long. Having broken windows not only draws energy, but also subconsciously let's you know that it's okay to not finish what you've started. Starting with a clean slate is a necessary condition for success in any new endeavors. In addition, the tiny successes brought by fixing broken windows create a positive feedback loop and it helps you complete even larger projects.
For the transition period, I think it's probably a better idea to save New Years' Resolutions until March. Take the first couple of months of the year to patch up anything left outstanding from the previous year(s) and start fresh, even if you are a few months late. I'd love to hear what other people think about this approach, so if you've had experience doing something like this, drop me a line in the comments or via email.