Luigi Mangione's pretrial suppression hearings in the New York state case against him are well underway.

A judge will decide whether some of the evidence will be excluded from trial, which is what the defense is arguing for. But with some of that evidence now accessible to the public, there are questions about how it will impact seating a jury.

CBS News New York's Alice Gainer has been in court every day of the hearings. She spoke with two attorneys and a jury consultant who work on high-profile cases.

A concern in cases like this is people trying to get on the jury to influence it or, as one of the experts said, for fame.

A short clip of police bodycam footage of Mangione's arrest, and photos of items police testified were found on Mangione when he was arrested, including a gun and a notebook, have already been released. So how will having details and evidence out there, all over social media and the news, affect finding a fair and impartial jury? 

"There are people who tune things out"

Legal experts say, despite all of the information about the case out there, they believe a fair and impartial jury is possible, though it will take specific questioning of prospective jurors to find them.

"There are people who tune things out and will come in and say 'I have no idea who this guy is,'" law professor and civil and criminal attorney Donte Mills said.

"You're going to have a lot of questions that have to do with individual jurors feelings with respect to insurance companies, their feelings with respect to people being armed," New York Law School professor Anna Cominsky said.

"One of the questions we ask is 'How do you get your news? What are your sources ? What are your apps?' And that question in and of itself tells a lot about people," jury and trial consultant Dr. Jo-Ellan Dimitrius said.

Dimitrius has worked on high-profile cases involving O.J. Simpson and Scott Peterson, and last year she consulted for the defense in the Daniel Penny subway chokehold trial. Penny was acquitted. She said sometimes having evidence out there ahead of trial can be a benefit to both the prosecution and defense.

"You're not going to be blindsided by what the other side has. You know what they have and you can potentially see how people react to it. So that's where you have a really unique opportunity in high-profile case," Dimitrius said. 

"We don't know what evidence is going to be allowed"

Mills said if some of the evidence is excluded in the Mangione case, that creates a potential issue.

"We don't know what evidence is going to be allowed in court and it does, you know, it clouds things a bit. Because there's gonna be some jurors, even if they say 'I can do it,' sitting in the courtroom saying 'But wait, what about -- I heard there was this notebook? You know, I never saw that, what about that? I wonder what was in there?' That's something you're going to have to contend with because evidence is trickling out in these earlier proceedings," Mills said.

"He has not even started his trial, so everything that we're hearing right now are allegations. The prosecutor still has to prove this case beyond a reasonable doubt," Cominsky said.

A trial date hasn't even been set yet.

Judges always remind jurors they're only allowed to consider what happens inside the courtroom when they deliberate.

Another interesting thing Dimitrius said is, often, in high-profile cases, jurors who are new to the country are selected.