I have played around with this concept for many years now. Unfortunately my results are in no way scientific. I have been able to show things like control of a pendulum that is not physically under a subjects control, the ability to influence things such as dice rolls, and the like. Small things. I have even done experiments where I have a pendulum suspended in a plexiglass box, so that no one is touching it or the table that it is on and no air can move it. Subjects can make it swing in one direction and then another on demand.
I have some friends that worked with Project Stargate, the governments remote viewing project, who say that there were instances of telekinesis there, but in all the records and reports from there I have seen I have found none. Lot's of spoon bending and remote viewing.
So, I would say that while some small things may be possible, you can't catch that falling pillar of stone, Yoda. :)