A "fundamental problem" can be found in any philosophy if you look hard enough, but you first must possess the ignorance to label it a "fundamental problem". The problem with the articles you listed is that they are not fundamental problems at all, but merely interpretations of her work by people who don't like her fundamental principals.
I don't consider myself an "Objectivist", because I will not adhere to what one individual or group decides is correct, nor will I weigh decisions based on them (e.g. what would Jesus do, what would Ayn Rand do, etc). Many critique Judeo-Christian beliefs by citing excerpts that contradict each other. So what? That doesn't mean the Ten Commandments are bogus - seven of them form the basis of all modern justice systems (I don't believe in any higher power/spirit/energy...so you can guess which seven I’m talking about:) ). A few fundamental principals of Ayn Rand's philosophy are:

--That humans beings are born with the capability to do great things. The human mind has endless capability, and that reliance on a higher authority or a supernatural being threatens and obstructs this capability.
--That capitalism is the greatest enabler of all because it is not a system, but simply the result of people left to their own devices.
--That by adhering to a moral and ethical code based on honor, clear thought, and motivation; humans achieve greatness.

I'll be honest; I didn't have the patience to do anything beyond skim over each of those articles. Socialists have always had a difficult time stating their TRUE BELIEFS:

--That government is more capable than individuals. That government has endless capability and that if the interests and production are decided upon by the state, everyone will be better off.
Rand's argument, which I agree with, is that this is an elimination of the most basic freedom: creativity.

---That people are weak and not able minded, so the government should disburse goods and services to ensure everyone makes ends meet, and is happy/healthy/etc.
How long does it take you to research what kind of car to buy? What about buying the car, getting insurance, and getting the oil changed? How about getting that vehicle registered? I'm not suggesting that we should eliminate the Bureau of Motor Vehicles (cut their budget, yes), but it is merely a comparison of a government provided good/service vs. free-market/profit driven good/service.

As far as the "good of the people" more specifically, try comparing the numbers of deaths at the hands of socialism and communism? How about we compare the opportunities for class mobility Western Europe (almost non-existent) vs. Eastern Europe (free market). Unemployment rates and GDP growth in Ireland vs. France.

---That capitalism is the greatest threat to people who are paid by the local, state, and/or federal government to sit around and talk about societal ills, the evil things people did years ago that we are apparently supposed to feel guilty about, and how we all could stand to live a little more meagerly and "give the people at the bottom a chance"
In pure capitalism these people would not exist because university students rarely take these classes unless they have to, and the ones who do take these classes rarely apply any specific skill learned in these classes in any profession outside of becoming a professional guilt inducer. Interestingly the people who do this the most are the ones who do not have to worry about anything in regard to their lifestyle or wealth (most notably Hollywood).

Before you cite specific examples of the failures of capitalism in America, keep in mind that there is no better proven system in the history of man. Like I said above, there are limits to objectivism. There are also limitations to capitalism. But the logical application and understanding of both are very empowering, and have positive impacts on your life (objectivism), and society (capitalism aka letting the capability of men reign supreme).


I'm interested to hear a rebuttal....I’ve yet to hear one from anyone after stating the above.

Children

Up until now, I haven't seen a coherent and logical rebuttal to the errors of objectivism voiced by rational people who actually do the hard work of thinking.

If there is so much doubts in your beloved philosophy, surely you must suspend your belief in it for a moment? This is the discipline of rational thinking.