It seems that to do shenanigans with Bitcoin would require the same care to avoid information leakage that would be required to do similar things with global digital payment networks and banks.
The key would be to begin by considering any address linked to an identity that is you or related to you "dirty," and to be careful about avoiding linkage to any of those dirty addresses. To really be careful I think you'd have to delve into graph theory and data mining a bit yourself, or follow the precautions of someone who knows what they're talking about. You'd also have to take care to pay attention to network addresses under the protocol, using Tor or similar proxying systems and considering any address that's been used from an IP that can be linked to you similarly "dirty." Use of VPSes that accept anonymous payment would also be an option, though again... don't SSH to them from your house! Use Tor or smurf the data around by way of proxies and drop sites and such.
Laundering money would require extreme caution to avoid such contamination, and would present many of the same challenges as money laundering in the fiat currency world. BTC/fiat conversions would be very risky. In-person BTC/fiat conversions are vulnerable to old fashioned gumshoe police work: "hey, that BTC you exchanged on localbitcoin... you happen to remember what that guy looked like?" These are also only feasible for small quantities. Large quantities would present a huge challenge.
What this really means is that Bitcoin is not intrinsically an instrument for villainy as some lazy press articles make it out to be. In fact, criminal use of Bitcoin requires orders of magnitude more technical sophistication, which the vast majority of criminals do not have. A highly educated or sophisticated criminal or intelligence network could surely pull off shenanigans with Bitcoin, but I doubt your average thug or child porn wanker is going to even comprehend the stuff I wrote above. So at the very least, Bitcoin is only a criminal tool for very geeky high-IQ criminals.