If a criminal uses Bitcoin to launder his funds, can the bitcoin network stop him from using Bitcoin? Can we close his account?
In reverse order.
Can we close a criminal's account?
The owner of a bitcoin address can move all the money out of the address and then delete all copies of the key pair for the address. This would amount to closing the account, as the likelihood of someone having the same address in the future is infinitesimally small. However, moving bitcoin money out of an address requires either the owner's consent or legal pressure brought bear on the physical human being assumed to own the account. Criminals are adept at avoiding this sort of pressure.
Can we stop criminals using Bitcoin?
This would require network consensus to collectively blacklist a bitcoin address. At current the community would be very unlikely to endorse such a protocol enhancement; as it could be used to tyrannise minority account holders.
If such a consensus was reached, locating criminal accounts would be difficult unless all residual mechanisms of bitcoin anonymity were also outlawed at the protocol level. Might as well rename the currency "1984".
Until bitcoin can be used in large volume to directly purchase food, shelter, safety and bling; criminals wanting to enjoy their ill-gotten gains have to change their bitcoins into a mundane currency like US dollars. Currency exchanges are already improving their recording and accountability to law enforcement officials. So the criminal will need to launder the money through plausible revenue sources before cashing out.
What can we do if Bitcoin is used for money laundering?
People or businesses could snub money that has come from a proven mixer or other aggregate wallets that don't comply to some auditing standard. But if bitcoin grows to any meaningful size, that is a lot of banking services or aggregate wallets to trace and enforce.
Considering how disposable each bitcoin address is, a botnet could simply create a million temporary accounts; feed the dirty money in at random; mix about like a mesh network of transactions following a plausible traffic pattern; and then spit out clean money.
In the long term, law enforcement will have powerful forensic tools to infer most cases of obvious money laundering. In turn, criminals with the connections and wealth will rent advanced money laundering methods as needed - like they already do in Vegas*.
* If you are suitably paranoid, you have to wonder how many bitcoin casinos have been established specifically to gestate money laundering operations.
It can't be closed, because there is no account. Likewise if he/she were using cash dollars for criminal purposes, it would not be possible to "close his wallet" as if it were some "account".
No one -- not a government, not the Bitcoin core developers -- can "close" a Bitcoin "account" because no central authority has unilateral control to do so. The closest it comes to "closing" an account is deleting the private key to an account, and such could only be done by forcing the holder to do so or tricking them into using a service that compromises their security by not really giving them control of their keys. Included in the latter would be government forcing intermediaries such as exchanges and services to comply and aid.
If someone is laundering money, it is likely necessary to catch them doing the actual illegal act of selling something illegally.
I have a third option: We get rid of Anti-money laundering (AML) regulations.
Money laundering has been criminalized in the United States since the Money Laundering Control Act of 1986. Perhaps it's time to reverse that decision.