Okay, but your client keeps a record of the addresses you have sent from? And your counter-party client keeps a record of addresses they've received at?
So to prove you transacted with said counter-party, authorities would need access to both to and from clients? (The wallet.dat x2?).
Not necessarily. Say at some point you purchased a DVD from an eCommerce provider who was also selling pirated software and got all his servers seized. In his transaction list would be:
SALE LEGIT_DVD 25BTC Your name Your address Date/Time
Or whatever, so they know at a given time you sent 25BTC to that provider. They can then look on the block explorer and see a 25BTC transaction at that exact moment from one of your bitcoin addresses to the site's bitcoin address, and "the man" how now tied your real name to your bitcoin address. Now all transactions in the block explorer with that address might as well have your real name.https://en.bitcoin.it/wiki/Anonymity
* cough! * Fake name!
* cough! * Only use the bitcoin address once!
The Man is now up against plausible deniability - "no, Joe Bloggs doesn't live here. Perhaps they lived here before me? No, I've never heard of "LEGIT_DVD" or this "coinbit" thing. Your search warrant says 'Joe Bloggs'? Well come back with a proper warrant with my
name on it and then you can legally execute a search. I'll be happy to let you examine my PC's hard drive if
you have a legal search warrant."
Even in a post-widespread-bitcoin-acceptance world you just need to make sure that you use multiple wallets, and the bitcoin wallet The Man catches you with isn't connected to LEGIT_DVD.
Incidentally, would The Man even be able to get a search warrant for a LEGIT_DVD purchase? Maybe in some jurisdictions, but in mine the judge signing the warrant would have to be asleep or incompetent (both possible, I'll admit...)