According to the New Zealand Herald, Kim Dotcom suspected he was being spied because of a 150 millisecond connection delay while playing his favourite game—Call of Duty: Modern Warfare 3.
Kim wanted to be the king of MW3 so hard that he had a dedicated internet connection that linked his Coatesville mansion directly to the Sky Tower in Auckland. This initially allowed him to enjoy just a 30 millisecond latency. However, that changed when New Zealand's Government Communications Security Bureau decided to intercept this link:
Information held by the Herald shows Gen-I studied data showing the amount of time it took information on the internet connection to reach the Xbox server. It went from 30 milliseconds to 180 milliseconds – a huge increase for online gamers.
The reason for the extra time emerged in a deeper inquiry, which saw a "Trace Route" search which tracks internet signals from their origin to their destinations. When the results were compared it showed the internet signal was being diverted inside New Zealand.
Apparently, New Zealand technology services company Gen-I was investigating these strange delays in November. That was before New Zealand's government official starting date for Dotcom's wiretapping.
If true, this may have violated Dotcom's civil rights. According to the New Zealand Herald, the episode is also bringing "fresh calls for an inquiry amid claims of the spy agency's role in the international "Five Eyes" Echelon Network." Echelon is the popular name for the telecommunications spy network established by Australia, Canada, New Zealand, the United Kingdom, and the United States. [New Zealand Herald via Betabeat]