Neither gravity nor momentum work that way. For one, if a thing is weightless, that doesn't mean it's massless. It is just as hard to stop a heavy object from moving (or changing its direction, or slow it down) whether there is gravity or not - this is inertia. With gravity, you have a constant force (hopefully) which gets stronger the more mass the object has, so there is more force to change it's direction/speed, and it would keep whatever on the floor; this is only a problem when you have to pick it back up, as you not only have the inertia of the object, but the force of gravity (and, as we are on a star ship with artificial gravity, we can just modify it locally and take care of that). Without gravity, the stuff (boxes, columns, redshirts) just flies through the air/vacuum, hitting whatever gets in its way until all it runs out of momentum (which is only taken away by hitting things). Here is a picture to illustrate:
On the bridge there shouldn't be anything that just falls; it can only be loosened by an explosion of some sort, and in the vast majority of cases would squish whoever was under it anyways.
Without air, however, there wouldn't be shock waves caused by exploding consoles (just electrical/plasma issues), so any of the above would be moot.