Everything is happening in June, yet in the beginning of the first day everything looks like it's winter, with no leaves on the trees, the way people are dressed, and so on. The show was filmed during January/February 2004.
In the fist part of the mini-series, J.T. Neumeyer promises his daughter that they will look for Orion with her new telescope. He is shown looking at Orion's Belt a little later that night. Orion's Belt is only visible from Washington in winter evenings, not June.
During the first hour, J.T. is shown in a flashback when his wife dies on 7 June 1994. The newscast in the background is reporting O.J. Simpson's family is begging him to turn himself in. The murders did not happen until 12 June 1994.