If I can say, a lot of it seems to be lack of understanding of police interrogation techniques, seasoned by already being convinced of GZ's guilt, before the records were released.
The interrogation tactic Serino and the Singleton use are classic techniques. I believe there is even a specific name for that procedure. Round 1: Singleton is all about just the facts and in round. Round 1 strays a little bit from the typical interrogation because it's not a classic 'who done it'. They know he shot Trayvon. Round 1 was just taking statements.
Round 2 is how a typical round one goes. 2: Serino is the confident and fast talking, but sympathetic buddy, who's only looking out for Zimmerman's best interest. He is not allowing GZ to tell his story, he is asking questions based on GZ's statement and he seems to be generally asking questions about excepted truths regarding the incident (how many times did you shoot?). This is to establish honest body language, later to be compared against perceived dishonest body language. Now remember, by this point, if I recall the chain of events correctly, Serino has already recommended manslaughter, as he states the entire situation could have been avoided, had Zimmerman stayed in the car. However, in the interrogation, he acts like he completely understands the situation. This is to establish trust. People are more likely to "do more talking" in that situation.
Round 3 is the walk through. This is to see how far from his original story, the timing and location vary. There will be variations because by now, Zimmerman's memory of the incident have already started to deteriorate. It's been almost 24 hours since the incident and he has already recalled the incident, at least twice. Here's the interesting thing; they expect discrepancies. If his story was perfect, every time, they would be more inclined to believe it has been memorized.
Round 4 is when they try to hit him. Now remember, Serino thinks this is manslaughter, at this point. They can make an easy case if they can just get Zimmerman to admit to instigating the incident. Notice he is pushing the guilt factor first (the Catholic questions are a big indicator), showing pictures of Trayvon (a highly questionable tactic, mind you because emotional manipulation is known to cause memory doubt), threatening with evidence they may have against him. Then he goes into minor inconsistencies that are probably no big deal. Help me help you. This is done intentionally to get the suspect to doubt themselves. Then he goes with the alternate theory tactic. "I know your history so I know you had good intentions..." Leaving the room, they are discussing his reactions and what they are going to do, next. In the beginning, Singleton is relatively silent. By the end of that interview, it went from minor inconsisencies to glaring inconsistencies where he is clearly lying. They do this on purpose. If they come at him too hard, in the beginning, he is more likely to shut down and immediately deny. Interrogators try to avoid putting them in the denial state because it makes the suspect reinforce their security in their innocence. By the end, though, they are going step by step, deconstructing every word Zimmerman said, making him doubt everything (such as the "they always get away" pointing out that they don't always get away. That's not even relavent to the case. They just want to make him doubt himself).
What I've seen so far in the investigation is that they did a pretty by the book interrogation. It does nothing for telling me what Serino or Singleton are thinking, it just tells me that they've had standard training in interogation. What does speak volumes, though, is after all of that, and Serino's recommendation of manslaughter, Serino still comes out and says, Zimmerman's story is supported by the evidence and witness testimony. Either Serino is lying about that to cover up or his recommendation for manslaughter had more to do with moral accountability than "blatant inconsistancies" in his story.