Yes, There are multiple cases in which Bitcoins can be used illegally. Bitcoins bring with it, a notion of anonymity which allows people to transact without revealing their identity. This privilege can be highly misused. However all exchanges in the world mostly are following Anti Money Laundering and Know your customer Policy to avoid any illegal activity by any user of Bitcoins.
Anonymous is the biggest bitcoin problem and very serious thing that must be immediately resolved, it's time to wallet provider verifying bitcoin user identity, so if there are problems of course can be accountable.
i do not think that it is a problems it is one of the best characteristic of bitcoin and most of the people like bitcoin because of its anonymity. if bitcoin will lost this characteristic then its popularity will also effect. therefore we can hope that bitcoin will continue its anonymity characteristic for ever.