Well... since this isn't in the "Master's" only section i'm going to chime in.
From my perspective it is both parties responsibilities, although i do believe it is not an equally shared responsibility but more of a 70/30 (or so) split with the Dominate having more of the responsibility depending on what the scene entails.
It is my responsibility, as a sub, to ensure that limits, fears, etc. are expressed to my Dominate and more importantly expressed in a way that he understands. It is also my responsibility to ensure that i know the Dominate enough to be secure in his judgment and secure in the knowledge that he is not only in control of me and the scene but that he is able to control himself as well. It is my responsibility to tell him when something isn't working, be it a physical, emotional, or some other reason.
The amount of responsibility changes though when certain items, such as bondage, deprivation of some senses, etc. are used. It is my responsibility to ensure he understands me well enough that when he does tie me up tight and i can't communicate (as well) he can still read and understand me.
The amount of responsibility changes as well when sub space is hit. At that point, he has taken me to the point that my judgement is impared. Even if things were to go wrong it may be several moments or even minutes before it would/could register with me depending on what the problem is. Therefore at that point it is imparitive (almost a 100% in my mind) that he be responsible for the entire safety of the scene.
*grinz* not sure that makes complete sense... but i know what i'm talking about... lol!