I particularly disagree with his latest post: Why You Should Never Talk to the Police. It's a short post, linking to two videos (each about 20 minutes long), and you'll need to watch the first one (Don't Talk to the Police by Professor James Duane) before any of the discussion makes sense. I've commented over there, but I think it's worth repeating my thoughts in my own blog as well.
I think there are a few issues here. (Disclaimer: I'm from the UK, so I don't have any personal experience of the US legal system.)
1) The title is ridiculously overblown, when Prof Duane (echoed by Mr Schneier) says that he will never talk to a police officer. For instance, if you were lost, would you ask a policeman for directions? Earlier this evening, I saw some police officers dealing with a guy who was lying on the ground (head injury), so I approached them and volunteered my services as a first aider; I then waited with him until the ambulance arrived. Is anyone seriously suggesting that I risked incriminating myself by doing this, and that I should have just carried on walking?
2) I think there's an important distinction between giving a witness statement and being questioned as a suspect. I witnessed an RTC (Road Traffic Collision) a few years ago, involving three vehicles. I gave a statement to the police, and technically I could have got in trouble (one of the indicators on my motorbike was missing), but the policeman didn't leap at the chance to arrest me, presumably because he recognised that I was doing him a favour. Also, even though I had nothing to gain from this, I helped the driver of the middle vehicle, because I saw that he had stopped in time - he was pushed into the front vehicle by the lorry behind. (I've elaborated on this in more detail in a previous post.)
3) The (physical) audience at Prof Duane's talk were all law students. As a defence lawyer, your job is to get your client acquitted, not to actually get the guilty person convicted, so it makes sense to "play it safe", and avoid anything with the slightest risk. As a member of the public, my priorities are different, and I'd prefer not to have axe murderers roaming the streets.
4) At one point in the video, Prof Duane gives an example of another lawyer who talked to the police, and then wound up with his word against theirs: they claimed that he'd admitted grabbing hold of someone, and he denied it. If we assume that this other lawyer was telling the truth, that means that the police made up the entire thing. If that's the case, what would he have to gain by refusing to talk to them? I.e. he could say "No, I never confessed to that, in fact I refused to talk to them at all", and it would still be his word against theirs.
5) I don't believe that the police are all out to convict innocent people. Going from personal experience, I was in a situation about 10 years ago when a prostitute tried to mug me on my way home: she threatened to stab me unless I gave her money. (Again, as regular readers will know, I've elaborated on this in a previous post.) I was able to run away, and I then called the police. When they arrested her, she claimed that I'd attacked her (and maintained this in court), so it was a case of my word against hers. I phoned the police in the first place (when I was safely at home), and I went along to the police station and spent several hours there, giving them a statement and being checked over by their doctor (for injuries matching her weapon). According to Duane and Schneier, this was a very bad idea, because I had nothing to gain, and everything to lose. Meanwhile, the lady in question refused to say anything (on the advice of her lawyer), and came up with a fairly elaborate story when it came to court. The judge made it clear to the jury that it was pretty suspicious for her not to have mentioned any of this when she was first arrested. Meanwhile, the police made it clear to me right from the start that they didn't believe anything she'd said, and that whatever happened in court, I'd be going home to sleep in my own bed that evening. The end result was that she was sentenced to 18 months in prison. So, leaving aside any issues of justice, and looking at it from a purely pragmatic point of view, I don't think that "refuse to speak to the police" was a particularly effective tactic there.
Bottom line: I think that if you haven't done anything wrong, and you cooperate with the police, then it will be better for everyone.