Thankfully, LA Noire offers some of the best facial animations in the industry thanks to MotionScan. When interrogating witnesses, as noted above, you need to watch their faces for discerning expressions.
Such is the importance of interrogation and investigation that you can actually skip an action sequence if you fail it three times and just continue with the story.
You'll need to pay close attention to a suspect or witness to see where they could be lying and press them further. You can either be nice to a suspect to gather information, go insane or simply accuse them of something that they or may not have committed. Unlike the original release, LA Noire Remastered now uses the Good Cop, Bad Cop and Accuse options when interrogating. Using information gathered up till that point can help your case.
Based on who you interrogate, you could either wind up with more evidence or accuse the suspect of the crime. Speaking of interrogations, LA Noire is full of them.