In reality, this supposed evidence would get thrown out of the courtroom about as fast as the case itself.
The Jury Won't Ever Be Told To Just "Disregard That Statement"
Imagine this: The prosecution has a videotape which shows the defendant killing his wife, but the police got the tape without a warrant and the judge decided it was inadmissible as evidence. So when the defendant protests his innocence, the clever prosecutor will proclaim, "The security camera video of you killing your wife says otherwise!" The lawyer will immediately be forced to "withdraw" this, and the judge will ask the jury to "disregard that statement," but the jury is now aware of a tape they weren't supposed to know about. A villainous prosecutor can flip this around and plant seeds of doubt about an innocent man by saying something that makes him sound bad, then immediately withdrawing their words, as if that somehow zaps them from existence.
In Reality ...
This is known as "unringing the bell," because a jury can't simply inflict amnesia on themselves because a judge tells them to. This, of course, can taint the result of a trial. In TV Land, either the judge's words magically solve the problem, or a lawyer gets away with being sneaky. But in reality, this would likely produce a mistrial, and might even raise the need for a new jury.
This one is a Law & Order favorite, but it also pops up in the supposedly ultra-realistic The Wire, when Omar gives false testimony to get Bird convicted. First Omar says that he met Bird in jail, implying a criminal history. The opposing lawyer objects, and the judge asks the jury to "disregard that statement." Later, Omar outright accuses Bird of murder, and the judge again asks the jury to pretend that baseless claim never happened. But it's all part of Omar's plan to make Bird look guilty. Bird is indeed found guilty, and the prosecutors later thank Omar for lying for them. And yeah, we get that the show explores problems within the system, but there's corruption and ineptitude, and then there's basic mistakes that would force lawyers and judges to look for new careers.