What are the problems with it?

1. Phorm intrudes on privacy. In BT's trials in 2006 and 2007, users were not told that all their web activity was being intercepted and and most of it read. Even in BT's 2008 trial when users' consent was apparently sought, they were not told clearly that all their web activity was being intercepted and most of it read. It is arguable that user consent for an intrusion at this level cannot be reliably obtained. The implications are so far reaching and the consequences so unpredictable that no one can reliably assess the risk.
2. Phorm exploits websites' material for economic gain without their permission. It uses private communications between those websites and their users to drive business to the websites' competitors. A company may invest a substantial sum on building and promoting a website. If accesses to that website are routinely intercepted for the benefit of their competitors, their investment is being hijacked and its value taken from them.
3. Phorm erodes trust in commercial communications. If you don't know who might be monitoring - or changing - your communications, you can't reliably do business. Although the Web is a new communications medium, the principles developed for traditional methods of communications still apply. Practices which have been outlawed for post and telephone are equally undesirable on the Internet. A key test is whether we would allow any process – such as interception – to be applied to letters or telephone calls. Phorm fails that test.
4. Phorm puts the reliability of communications at risk. It introduces the ability to change data as well as reading it. Indeed, in BT's 2006 Trial, messages from users to websites were actually altered by the Phorm system, all be it accidentally. If systems such as Phorm are deployed, commercial pressures may lead to non-accidental altering of messages. If data is changed between users and the websites they visit, some websites may stop working.
5. Phorm puts the security of communications at risk. Its interception of communications presents opportunities for abuse from within Internet Service Providers and Phorm itself, and also from external hackers and fraudsters. Internet Service Providers using Phorm would be more vulnerable to criminal and cyber-terrorist attacks.