I think it's worth taking a step back from the details of any one of Derren Brown's effects, and looking at the nature of stage magic. A stage magician employs a set of techniques called misdirection to mislead the audience as to how a trick is performed, to direct their attention to irrelevant aspects of the performance, or to encourage them to misinterpret relevant aspects.
An important technique in misdirection is to provide the audience with a false explanation for how the trick is done. A magician who says that a trick is done by magic encourages you watch carefully at the point where he waves his magic wand (knowing that this does the audience no good, because the rabbit was already loaded into the hat). A magician who says that a trick is done by science encourages you to look at the fancy gears of his machine (when actually there's an assistant hidden inside). A magician who says that a trick is done by psychic powers encourages you to watch carefully at the point where he concentrates on reading the subject's mind (when actually the card was marked or forced).
Knowing all this, as I imagine you do, what are we to make of a magician who explains that a trick is done by psychology? I guess this time he might be telling the truth, right?
Now, let's look at your examples with the above in mind, and ask some questions.
In the first example, why does David Frost later agree that he was thinking of a place, after first denying it?
In the second example (guessing the pet name),
In the third example (the creepy clown),
I'll ROT-13 my own answers to the questions, but I strongly recommend that you do your best to figure out your own answers to them before decrypting mine. Trying to figure out plausible mechanisms for magic tricks is a way of calibrating your rational thinking skills, in the presence of an adversary (the magician) who is trying to use all your perceptual biases and cognitive shortcuts against you. If you find yourself seriously considering hypotheses like micromuscle reading or subliminal suggestion, then that's probably because the magician has managed to...
I just want to burn him at a stake and watch his witch's heart bubble. It’s extraordinary. Great trick. - Stephen Fry
Derren Brown does many amazing tricks - I want to focus here on his "mind reading". This is way beyond any cold reading I've seen, but he insists that he uses no actors or stooges. He's also a skeptic, very clear about not being psychic. He does reveal some of his tricks, but maintains a lot of mystery.
Reading David Frost's mind - unusually, he struggles and gets the first one wrong, and seems to reveal tiny glimpses of his technique. Then at the end he gives more hints about his technique than usual.
Pet name - getting someone on the street to read another person's mind. In the full version (from the DVD of Trick of the Mind, series one) the segment starts with Derren telling the guy (the pet owner) that sorry, it won't work on you, then later changing his mind and bringing him in.
Creepy clown - the detail here is extraordinary.
Watch the videos then scroll down, if you want to watch it without being influenced by me... I have a few thoughts, but they don't go very far in explaining it...
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Whatever he's doing, he's extraordinarily good at it. Some speculations: