It always seems a little odd to me that bitcoin is associated with criminal enterprise. Surely with the transaction record public, it's rather easier for the police to "follow the money" than with cash etc?

You can "follow the money" electronically, but unlike bank transfers there's no physical connection. Going from imaginary point 1 to imaginary point 2 doesn't really tell you anything.

But some transactions are ultimately linked to the physical world, and that gives a window through which more can be pinned down over time. Operating from just the blockchain doesn't tell you very much, but combined with other things it's a lot more informative than cash movements. You're never leaking less than you think.

Bitcoin mixers can make it almost impossible for people to follow bitcoin transactions, providing that the number of coins in the mixer far exceeds the amount you are trying to mix.

Again, you're never leaking less information than you think. I also expect that using bitcoin mixers will be prosecutable under AML laws in the medium term, if they aren't already.