What are two reversible errors that an appeals court might grant to someone convicted of a crime? Provide a hypothetical example of each.

Reversible errors in a criminal case that an appeals court may consider sufficient to overturn a conviction usually result from the denial of a defendant's constitutional rights, which in judicial parlance are called "structural errors."
An example of a structural error that deprives a defendant of their constitutional rights would be if the appeals court found racial discrimination in the selection of a grand jury that issued the indictment. The US Supreme Court found in United States vs. Gonzalez-Lopez (2006) that structural errors that increase "the likelihood of a trial outcome unfavorable to the defendant” must lead to the overturning of a conviction.
Ineffective assistance of counsel is another common structural error cited by defendants when appealing a conviction. An example when ineffective assistance of counsel would be not providing a defendant information about a potential conflict of interest—say, a prior working relationship with one of the prosecution witnesses.