When Marty is watching the VHS, the camera cuts between the television and his face. The digital counter on the video player repeats the same sequence of timings but shows a different picture on the screen.
Marty refers to the day he was interviewed by the detectives as 'last Saturday'. May 1st, 2012 was actually a Tuesday.
The original investigation was in 1995. Rust Cohle drives a red F250 heavy duty. However, the F250 was not available in the "heavy duty" version until 1997.
There is a jukebox in the bar at the beginning where Rust and Marty meet to talk. Initially the jukebox is a CD jukebox as you can see the track listing cards for full CDs. Then the jukebox switches to a 45 rpm/7" record jukebox as you can see the record being played.