In the 1998 case of Ellis E. Neder, Jr. v. United States, the Supreme Court ruled that failure to instruct a jury on an essential element of an offense in a federal criminal trial is subject to harmless-error analysis under Federal Rule of Criminal Procedure 52(a). The defendant, Neder, was convicted for various fraudulent activities related to real estate transactions but argued his conviction should be overturned because the jury wasn't instructed they needed to find "materiality" as part of their decision-making process - something he claimed was an essential element of fraud charges against him. However, the court held that while this omission was indeed error and materiality is typically considered part of fraud offenses; it did not automatically require reversal if it could be determined beyond reasonable doubt that this error didn’t contribute significantly towards his conviction (harmless-error rule). In other words, even without considering materiality aspect explicitly during deliberations; there's no reasonable probability that outcome would have been different given overwhelming evidence presented against him.

In the dissenting opinion for Ellis E. Neder, Jr. v. United States, Justice Stevens argued that materiality is an essential element of fraud and should be included in jury instructions during a trial for mail fraud, wire fraud or bank fraud under federal law. He stated that omitting this requirement could lead to wrongful convictions based on trivial falsehoods which were not actually capable of influencing decisions or causing harm - thus failing to meet the standard definition of 'fraud'. Furthermore, he pointed out inconsistencies in how different elements of these crimes are treated by courts; while some aspects are considered crucial enough to require proof beyond reasonable doubt (such as false statements), others like materiality have been overlooked despite their importance in establishing fraudulent intent and potential damage caused.