My take on Bobby Dassey:
Please keep in mind that this is based on just reading the trial transcripts. I can't see any photos, videos, or any other exhibits that were entered; I can only read descriptions of them. I'm also comparing the transcripts to how the events were depicted in the show, and I'm doing that from my memory of episodes I watched only once, and that was a few weeks back. If my memory is faulty, please feel free to correct me.
Bobby Dassey has become a popular subject of alternative killer theories. One of the reasons why is that the series presents a moment in court where Dassey, under direct examination by Ken Kratz, relates a "joke" that Steven Avery told about "getting rid of" a body in the days following Halbach's disappearance. This sets off a relative firestorm in the courtroom. Strang and Buting object and inform the judge that the only mention of this "joke" in any of the police reports came from a Michael Osmunson, a friend of Bobby Dassey.
Osmunson told investigators that, on November 10th, well after Halbach had been reported missing, he and Bobby Dassey were hanging out in the Avery garage when Steven Avery walked in. By that point, the Halbach disappearance was all over the news, as well as the fact that Steven Avery might have been the last person to see her alive. Osmunson jokingly asked Avery if "he had the girl in his closet". Avery jokingly responded by asking if Osmunson and Dassey wanted to help him bury the body. Dassey never mentioned the comments to police, but Osmunson's statement made it clear that Dassey was a party to the exchange.
Now, it is critical to note that Osmunson could not have possibly been correct about the date of this conversation. By November 10th, Steven Avery was already in custody.
Back to the trial. During direct, Kratz asked Dassey about this conversation. He specifically asked Dassey about a conversation on the evening of November 3rd. That's when Dassey said "It sounded like he was joking, honestly, but he asked us if he wanted us to help him get rid of the body." No context is given for this comment. Boom, immediate objection from the defense.
The date issue is critical here. Halbach was reported missing on the morning of November 3rd. Her disappearance would have barely made the news cycle by that evening, so it is extremely unlikely that Dassey or Osmunson would have known about it to bring it up with Avery. Avery's comment in that context is incredibly damning. However, Kratz also had the date wrong. Dassey was at work on the evening of November 3rd, so the conversation could not have happened then either. After much discussion, both the prosecution and the defense agreed that the conversation happened on the 4th, when Dassey could have been present, and Osmunson could have known about Halbach's disappearance. It is really important to note that both sides agreed upon this date.
So, the defense has objected on grounds pertaining to the rules of evidence (I'm not a lawyer, so I'm simply trying to summarize what I read). If a statement by the defendant is going to be entered into the record by another witness, then the State is obligated to report that to the defense during discovery. The State never alerted the defense that Bobby Dassey was going to mention that joke. As I noted before, Dassey had never mentioned the joke to investigators. The defense asks for a mistrial because the jury is tainted by this information.
MaM edits out the majority of the debate over the defense's objection. The series gives the impression that the defense has accused Bobby Dassey of lying about Avery's comment, and that the State has perhaps suborned perjury by allowing Dassey to place the conversation on November 3rd. The truth is not nearly as dramatic. The defense does not accuse Dassey of lying. Rather, they accuse the State of not following the rules of evidence. The defense knew about the joke, as they'd seen Osmunson's statement. But they knew that the State hadn't put Osmunson on the witness list, so they assumed that it wouldn't come up. The defense certainly wasn't going to put him on the stand to detail their client joking about burying a body. But the State had an obligation to alert the defense that Avery's statement was going to come in via Bobby Dassey. The defense didn't think Dassey was lying about hearing the joke because Osmunson's statement placed Dassey in the garage when the conversation happened. But they were blindsided by the statement because of the State's failure to disclose that it was coming. It should be noted that the defense never interviewed Bobby Dassey before the trial, despite knowing that he was a witness, and despite knowing that he'd heard the joke. The defense assumed that the joke wouldn't come up since the State didn't disclose it, and they should have felt comfortable in that assumption. But still, they had the chance to talk to Dassey and they didn't.
The series makes it seem like the judge simply dismisses the defense's request for a mistrial, and simply allows Dassey's (likely perjurious) statement to remain on the record. This is a complete distortion of the truth. The judge actually acknowledges the State's failure in reporting the discovery to the defense, and sustains the defense's objection. But he doesn't grant the mistrial because, despite the State's misstep, no one is accusing Bobby Dassey of lying. Instead, he ends court early for the day and grants the defense the rest of the afternoon to interview Dassey, and rules that Dassey's cross-examination will begin the next morning. He even makes the incredibly generous decision to prohibit anyone from the State from talking to Dassey until after the defense has finished with him. I learned all of that from the transcripts. The series makes it seem like the judge overruled the defense's objection, and the trial kept right on moving.
So, cross-examination occurs when court resumes the next morning. The defense gets Dassey to clarify the date of the conversation as being after Halbach's disappearance had hit the news, and that Avery's comment was likely a joke made response to a joking question. But it doesn't end there. The defense then brings up the issue of putting Osmunson on the stand. The State doesn't even force their hand on the subject. The State stipulates to Osmunson's likely testimony, and Strang is allowed to read a statement directly to the jury that says basically "There is a guy named Mike Osmunson, and if he were to testify he'd tell you..."
tl/dr: The series made it appear that Dassey was lying about hearing the joke and the judge let it stand despite the defense's objections. The defense was blindsided and was not give the opportunity to correct the issue on the record. That did not happen, at all.