The larger distinction is what is the purpose of the meeting. The Pope met with Castro (there are pictures). Carter met with Kim Jong Il on a semi-official meeting (although he acted a bit ultra vires). Nations and their representatives must occasionally break bread with the not so nice as part of statecraft.
The point of the Rumsfeld meeting is that we at one time were allies with Saddam, during a time that his behavior was not too different from today. Personally, I have little problem with that. Though in an ideal world we would never make common cause with tyrants, the real world is not so neat. Neihbuhr's "Moral Man and Immoral Society" lays out why the state cannot follow individual Christian mortality with respect to aggressors.
Sadaam was fighting Iran, who was our big enemy at the time (snarky aside - not so big an enemy that we would sell them arms and let them off after they killed 241 Marines). I have no problem with our alliance with him at least until Halabja an 1989. Presuming Halabja never occurred, I have no problem with suddenly turning on him after Kuwait (though April Glaspie should have been clearer) - Kuwait was an ally we swore to protect. No problem, IMO, that we switched on him for that.
What is poignant about the Rumsfeld photo is that Republicans especially love to personalize and demonize statecraft. They love to pretend that they dont deal with bad people, and that they recognize them. The reason for this self-deception is twofold, IMO. First, all Presidents have to sell war, and they usually do it on human rights grounds because our nation is laudably sensitive to such concerns. That this President elected to expand the deception to inventing security threats was a bit of an extension, but everyone talks about the baddie we are against, and it is always helpful to personalize the evil, even if that's not totally accurate. The problem is that the true believers in this President, the true "base", like some on this thread, are especially infantilized in their worldview, and they actually internalize this stuff as true. The other factor at work is that this particular President is also more susceptible to this worldview - he "looks into the eyes" of Putin, a tyrant in his own right, and sees a buddy he can work out with. He "hates" Kim Jong Il because he's fat and starves his people. It is like having your foreign policy run by a 14 year old, but that's what we are stuck with.
So when the President makes such a deal that we must invade Iraq because the deranged Sdaam is so uniquely malevollent, it makes sense to point out that this spawn of Satan was a handshake type of cuddle up to guy not long ago. Presumably, the Reagan Administration lacked GWB's charism of scrutatio cordium, his ability to gaze into the eyes of an adversary and discover his true character. Reality is always more complex than he or his true believers elect to understand.
Bottom line, don't regurgitate the talking points or talk about "birds of a feather". Those more grounded understand that you have to deal with the Devil occasionally, to paraphrase Churchill justifying the Alliance with Stalin. They also understand that you have to meet to express anything greater than rhetoric, like the Pope understood.