How long have you got?
As for her modes of thinking that she really shoves down one's throat, I partially agree and partially disagree. The 'mode of thinking' she really supports is that things exist objectively. People who say 'there is no right or wrong', or 'There is no objective reality', or 'perception is everything', or 'facts are not as important as feelings' etc., are all dicks. This is something that I can agree with I am a strong believer that things do in fact exist independently of our awareness and perceptions.
She was also a believer in rights - predominantly that those who had created something had the right to ownership of it. Now this unfortunately made her call on government to protect abstractions such as intellectual property, but by and large that notion remains applicable to this day. To suggest that this is 'outdated' is somehow to say that once, people did have a right to their belongings but now that we are 'enlightened', we can see that people actually have no claim to that which is theirs. Nonsense, as anybody can see.
This is the philosophy that underscores free market capitalism - that, regardless of outcome, one's right to property is inviolable by any other individual who can forcefully remove that property from you.
There are, however, several problems with her philosophy. While claiming to be for individuality, she was remarkably hostile to those with different aesthetic preferences to her. Stemming from the idea of rational, absolute, universal truths of logic, came this bizarre hatred of anybody with a different view to her on things from art to music to architecture, and the claims that they despised life and reason, and all this totally irrational nonsense. Now I'm all for calling a spade a spade and acknowledging when some music is genuinely terrible, but the idea that anything I dislike is automatically a denial of life... well, it's just mad.
And then there's her perversion towards gold. And, in fact, money. Yes, money is the central thing that brings economies and economic activity together, but it doesn't mean it's the sole thing which governs humans and human activity. She accurately gauged the morality of economic activity (as I mentioned before with the property stuff, and also that transactions must only ever be voluntary - this is quite ok), but then extrapolated that so that it was somewhat the only morality of all human activity. This is just weird. The goal of making money is quite a legitimate (and anything but immoral) goal when voluntary transactions are occurring (just by their very nature). But to say that the goal of making money is the only noble goal for humans, well, that just doesn't follow logically.
Then there are her assertions about gold. For somebody so staunchly anti-conservative, she really likes enforcing the preservation of monetary history. While it is true that economies around the world have largely used gold as a medium of exchange (due to several qualities it possesses - it can be minted, divided, weighed, and it is generally considered desirable), she takes from that the idea that gold is therefore the only acceptable medium of exchange. In contrast with an alternative, such as fiat money, yes, gold is the better option. But her addiction to gold is a fetish, and is not consistent with the rest of her philosophy.
For example, she strongly opposes religion, dismissing it as irrational and inconsistent with objective reality. But, all civilisations (correct me if I'm wrong) have all adopted a form of religion to explain the universe. Does this mean that, like her obsession with gold, religion must be the best option? No. Her positions on the two are inconsistent, despite her apparent hate for inconsistency.
The point is, she's far from perfect. But she's definitely relevant. Reading Atlas Shrugged, I was rather surprised at how much of it was spot on with what was going on in the economy at the time. This was reflected in the sales of that book, which skyrocketed during the crisis. Every politician could get a lot from reading some of her stuff. But, there are better things to read. Secondly, her zealotry, and the cult of personality around her, really turns people away from her stuff.
And her writing isn't very good. Enjoyable, but not good, literarily (is that a word?) speaking. I really enjoyed the books, but to be honest, you could do away with most of the philosophy in there. Rather than developing concepts through the book, every character is thoroughly one-dimensional, and they hammer the same words into you again and again and again, so after you've met all the characters and assumed that the bad ones will fuck the world up while the good ones will be good, you've pretty much got the novel down, so you can spare yourself the other 1,999 pages.
There are a million criticisms one could throw at her. Some of them would be highly valid. But to respond to your statement that she purports outdated modes of thinking, I'll have to disagree. The inconsistencies and failures of her philosophy are not a result of time, they are a result of logic (or lack thereof). The truths in her philosophy are similarly, a result of logic, not time, and are very relevant today.