Under s6, the Investigatory Powers Commissioner can opt to levy a fine (monetary penalty notice) if an interception occurred without lawful authority (defined in s5 - basically that a warrant is in place), but wasn't intentional. i.e. if a cockup happens and you accidentally intercept someone/something you shouldn't have. However, s6(3)(c) gives a get-out-of-jail of if the person was making an attempt to act in accordance with a warrant, so not all cock-ups are covered.
Appeals would go through the First-Tier Tribunal, which is a court of law. Essentially the situation is like a fixed penalty notice.
If the interception was intentional, and without lawful authority, then it's a crime under s2, with 2 years in jail and/or a fine as the penalty.
In this particular case, it appears that a warrant would have been present, but wouldn't have gone through the process correctly. I'm not sure therefore whether there was, or was not "lawful authority". Yet another bit of the IP Bill that needs proper definition. Ho hum :)