In a criminal trial the prosecution has the burden of proof on the existence or nonexistence of elements or facts essential to guilt.

Fed. R. Evid. 103(a) ("Rule 103. Rulings on Evidence (a) Effect of erroneous ruling. Error may not be predicated upon a ruling which admits or excludes evidence unless a substantial right of the party is affected, and (1) Objection. - In case the ruling is one admitting evidence, a timely objection or motion to strike appears of record,...If an opponent of evidence wishes to preserve a claim, for later review, that a trial court erred in admitting evidence, the opponent ordinarily must object to the offered evidence before the trial court rules that the evidence is admissible. If an opponent fails to make such an objection, the opponent will ordinarily be said to have waived or forfeited its claim that the trial court erred in admitting the evidence.

United States v. Beverly, 5 F.3d 633, 639-640 (2d Cir. 1993) (upholding trial court's ruling which allowed the government to use evidence of the prior shootings to impeach defendant's testimony because defendant had "got....If a trial court admits inadmissible evidence but later in the trial recognizes its error, the trial court has the discretion to allow an opponent to introduce otherwise inadmissible evidence to "cure" or ameliorate the harm done by the opponent's use of inadmissible evidence but the trial can or should allow the admission of curative evidence only if it concludes that the admission of curative evidence will not cause undue prejudice, delay, or confusion and will not do more harm than good to the goal of accurate fact finding.

Fed. R. Evid. 804(b)(1) ("Former testimony. Testimony given as a witness at another hearing of the same or a different proceeding, or in a deposition taken in compliance with law in the course of the same or another proceeding, if ..., in a civil action or proceeding, a predecessor in interest, had an opportunity and similar motive to...The hearsay exception for prior testimony applies in a criminal case only if the if the party against whom the testimony is now offered had an opportunity and similar motive to develop the testimony in the prior proceeding by direct, cross, or redirect examination. The exception applies in a civil action or proceeding only if the party against whom the testimony is now offered or a predecessor in interest had an opportunity and similar motive in the prior proceeding to develop the testimony by direct, cross, or redirect examination.