Serial is not a science podcast per-se, but includes a great deal of questioning and true investigative journalism. This is not all that different from science where questions are asked and an investigation is undertaken to attempt to answer the questions.
The first season of Serial details the arrest and conviction of Adnan Syed for the murder of his ex-girlfriend, Hae Min Lee in 1999. Syed continues to claim innocence. The podcast is produced by the producers of "This American Life" podcast, another good podcast. The investigators show no bias. They simply ask questions and investigate, looking for answers. The first season of Serial contains 12 episodes, all of which are between 30 and 60 minutes in length. I won't give anything away, but the season leaves you with many questions that simply do not have answers at this time. Excellent podcast!
The second season, which I have yet to listen to, focuses on Bowe Bergdahl, the U.S. soldier imprisoned by the Taliban for 5 years before being released. The controversy behind this story is that he is accused of willingly abandoning his post in Afghanistan and thus should not be celebrated. I'm waiting for the season to finish with plans to then binge listen!