Heinlein is considered a fairly "libertarian-leaning" author. Were there many mentions or references in his works of either Ayn Rand, her works/heroes, or Objectivism (explicit mentions, not merely espousing same/similar philosophy)?
I can think of one - in The Moon Is a Harsh Mistress, Mike is characterized by Mannie as "our Scarlet Pimpernel, our John Galt, our Swamp Fox, our man of mystery", therefore RAH was obviously aware of Rand's work.
The most explicit mention is in Moon when Prof de la Paz and Wyoming Knott are discussing politics during their initial meeting in Hotel Raffles. When Knott asks as to what Prof's political philosophy is and he replies "Rational Anarchist". To which she then asks if he means "Randite". My supposition has always been that this is referring to Ayn Rand. To which Prof replies that he and Randites can get along.
The only philosophical elements that Rand shares with Heinlein is the idea of self reliance and rational self interest. They both believed that that only duties chosen voluntarily were really worthwhile, and that only free individuals could really choose those most worthwhile values.
Beyond that, Rand was an atheist who viewed altruism as immoral, while Heinlein's Stranger in a Strange Land is a wholesale indictment of Rand's assertion that altruism is a fake value. He also firmly endorses religion in this book, even to the point of making his protagonist into the Archangel Michael. Heinlein also clearly thought very little of those who rejected such values as duty, honor, patriotism, and self-sacrifice, as seen in Starship Troopers. This makes it likely that Rand would have considered Heinlein “ultimately an altruist” and thus abhorrent to her view that the individual mattered more than the group in all circumstances and that any system of values which rejected that was oppressive.
The character in The Moon is a Harsh Mistress, compared to John Galt, has been noted to have been a computer in an attempt to satirize Rand's work. Further, in Beyond This Horizon, all basic human needs are free, and one character is quoted as saying, in a shocked tone of voice: “Naturally food is free! What kind of people do you take us for?”
There are vague philosophical similarities between AR and RAH, but they only serve to accentuate the significant differences.
Free love and self-reliance is about as far as they go together.
Ayn Rand never really "examined her own premises" as she so often recommended to dissenters from Objectivism. RAH seemed to have a grand time bouncing his left/right wing ideas off of each other.
