The appeal alleges Simpson's conviction in a hotel room confrontation with two sports memorabilia dealers was tainted by judicial misconduct, a lack of racial diversity on the jury and errors in sentencing and jury instructions.
The document criticizes Clark County District Court Judge Jackie Glass and accuses prosecutors of improperly questioning witnesses about allegations of intimidation.
It could take a year or more for justices to issue a ruling.
The former football star was convicted last October and is serving nine to 33 years in state prison.
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