Saul Kripke, the fixed referent for the man in this world who wrote Naming and Necessity

Agree:
"I will argue, intuitively, that proper names are rigid designators, for although the man (Nixon) might not have been the President, it is not the case that he might not have been Nixon (though he might not have been called 'Nixon')."
Kripke is putting forth this idea of how we should think of properly named things in all possible worlds. It is the case that for some x, in this case the man with the proper name Nixon, we rigidly designate as Nixon. Because in this world, the man is called Nixon, we refer to the man in all possible worlds as Nixon regardless of the properties or the name that person has in those other worlds.
I agree with this, because it takes a fairly practical stance on possible worlds where we in some sense privilege the actual world we live in by using this world as the starting point where we talk about things in other worlds by identifying things as they pertain to this world

Disagree
"How can I identify this table in another possible world, except by its properties? I have the table in my hands, I can point to it, and when I ask whether it might have been in another room, I am talking, by definition, about it. I don't have to identify it after seeing it through a telescope . . . Some properties of an object may be essential to it, in that it could not have failed to have them. But these properties are not used to identify the object in another possible world, for such an identification is not needed. Nor need the essential properties of an object be the properties used to identify it in the actual world, if indeed it is identified in the actual world by means of properties."
This quote too extends from the point of the quote above where we suggest that we can locate things in other worlds by locating them in the actual world. He explicates further that the way in which we identify things in this world is not by their properties but by a brute identification of it in this world for it may not be the case that what is identified in the actual world has those properties in other worlds.
This point just seems to be a rather philosophically lazy way of describing how identity works between what we locate in this world to how they are in fact the same thing with perhaps different properties and names in other worlds. We seemingly can suggest that something in this world can have an identical correspondent in another world without certain properties, but it seems rather unexplored how this is the case.