I’ve followed the debate on Hayek with interest, including contributions from Jason Soon, Tim Dunlop and Ken Parish, but I must say that I’m considerably less favorably inclined to Hayek than anyone who has written so far.
For me, any assessment of a political philosopher must look at actions as well as words. The obscurity of language in Heidegger can’t conceal the fact that he accepted the rectorship of Freiburg University from the Nazis and persecuted his Jewish colleagues. Given this fact, it’s necessary to read Heidegger’s thought in a way that brings out its antihuman and antidemocratic basis.
Hayek’s Freiburg is his support for the Pinochet regime in Chile, symbolised by the decision to hold the meetings of the Mont Pelerin society in Vina del Mar, Chile in 1981, at the height of the dictatorship. Hayek’s view was summarised in an interview he gave to the progovernment newspaper El Mercurio (there weren’t of course, any antigovernment newspapers at the time) in which he was reported as saying Mi preferencia personal se inclina a una dictadura liberal y no a un gobierno democrático donde todo liberalismo esté ausente. cited in Juan T. López, “Hayek, Pinochet y algún otro más”, El País 22 June 1999. A rough translation is ” My personal preference inclines to a liberal dictatorship and not to a democratic government where all liberalism is absent ”
I should say that, despite a fair bit of effort, I haven’t been able to verify this quote, but it’s been widely circulated and never denied, and the Mont Pelerin meeting in Chile certainly took place. My secondary source is here.
In reading this quote, we should note that ‘liberalism’ can only be understood in terms of free-market economic policies, since the Pinochet government was not in the least liberal in relation to freedom of speech and political action (in contrast, with, say, the undemocratic but generally liberal government of 18th century Britain).
With this clue, we can read Hayek’s work such as Constitution of Liberty and see that his support for liberal democracy in the ordinary sense of the term was weak and highly qualified. In relation to democracy, he argues:

“If only persons over 40, or income-earners, or only heads of households or only literate persons were given the vote this would scarcely be more of an infringement of the principle [of democracy] than the restrictions that are generally accepted. It is also possible for reasonable people to argue that the ideals of democracy would be better served if say, all the servants of government or all the recipients of public charity were excluded from the vote. If in the Western world universal adult suffrage seems the best arrangement, this does not prove that it is required by some basic principle.”

Treating the weasel words “it is also possible for reasonable people to argue” as a dishonest way of saying “I think”, it seems clear enough that Hayek is willing to countenance any abridgement of democracy that is likely to support the political outcomes he favours.
On liberty, Hayek reverses JS Mill, arguing that restrictions on intellectual freedom and freedom of speech are less important than restrictions on freedom of action, that is, intervention in markets. The natural implication is that, where speech endangers free markets it can legitimately be suppressed.
Two elements of Hayek’s thought are important here. First, his antirationalism leads him to discount Mill’s main argument for free political speech, namely that free discussion leads to better political choices. If order is spontaneous, talking about it is at best futile and at worst dangerous. Second, there is the (inverse-Marxist) materialism that emerges in full flower in public choice theory, where all political speech is mere camouflage for the nefarious activities of some interest group or other.

In conclusion, I think that Hayek’s support for Pinochet was a natural consequence of his system of thought and not an aberration. The same is true, in my opinion, of Thatcher, a similarly authoritarian free-marketeer.

I don’t want to argue, by the way, that any association with a dictatorial regime necessarily implies support for dictatorship. In some cases, particulary in relation to Stalinist Russia, there may be nothing more than foolishness involved. Gullible but well-meaning people like the Webbs were fooled into believing that the Soviet Union really was a workers paradise, based on the principles of liberty, equality and fraternity. At a more limited level, Milton Friedman defended the role of the ‘Chicago boys’ in Chile by arguing that he would give the same economic advice to any government, democratic or not, and that he had in fact advised the government of China. While this is dangerous ground, if you believe that you can make people better off by advising their government, it’s arguable that you should do so even if the government itself is a bad one. But I don’t think this kind of defence can be made for Hayek.