1) “Snowpiercer” season-finale, 9 p.m., TNT; rerunning at 10:03. For three seasons, this mega-train has spanned a frozen world, holding the only survivors. But now comes the confrontation: On one side is Wilford (Sean Bean), the train’s creator and despot; on the other are Layton (Daveed Diggs, shown here) and the rebels. Layton feels a New Eden micro-climate is livable; Melanie, a master engineer, disagrees. A final face-off looms, in an hour that is beautifully written and executed.
2) “American Idol,” 8-10 p.m., ABC. As “Hollywood Week” begins, past contestants arrive as mentors. There’s Ruben Studdard, the second champion (in 2003) and other winners – Jordin Sparks (2007), David Cook (2008), Lee DeWyze (2010) and last year’s champ, Chayce Beckham. Also included are Lauren Alaina and Haley Reinhart, who were second and third (to Scotty McCreery) in 2011.
3) “NCIS” and “NCIS: Hawaii,” 9 and 10 p.m., CBS. For the first time, these shows have a full-scale crossover. That starts with Torres (Wilmer Valderrama) getting a call from Hawaii: Tennant has a lead on a witness, from a case they worked five years ago. It reunites a duo that used to be called T’n’T. In the second hour, Knight (Katrina Law) flies in with more key evidence.
4) Documentaries. On the day after the Academy Awards, we can catch two of the nominees. At 6:30 p.m. ET, NBA TV has “The Queen of Basketball” – a short-documentary nominee about Luisa Harris, the only woman officially drafted by an NBA team. (That was in 1977; Harris, who died this year at 66, became a high school teacher and coach.) At 10, PBS has “Writing with Fire,” about women in India who buck biases to run a news website.
5) “Chelsea Detective,” any time, www.acorn.tv. Here’s the last of the year’s “Chelsea Detective” movies, an OK tale that’s a notch below the others. Fortunately, this streamer also has the previous three, which are first-rate. And next Monday, it will launch Jane Seymour’s “Harry Wild” mysteries.