Coleman attorney Joe Friedberg argued that counties were inconsistent in the way they decided whether absentee ballots were filled out properly and should be counted.
"Twelve thousand citizens who made good-faith efforts to vote were disenfranchised, with a variety of reasons," Friedberg said.
Franken attorney Marc Elias argued that Coleman's team has failed to show specific voters were disenfranchised, but only broad categories of mistakes that might have left some voters behind.
"This isn't evidence, this is an argument," Elias said.
Coleman, whose term in the Senate expired in January, trailed Franken by 312 votes after a recount and his lawsuit challenging the results of that recount. He wants the justices to instruct the trial court to open more rejected absentee ballots.
Franken hopes the court sweeps aside the appeal and orders that he immediately receive the election certificate required to take office. Franken is the potential 60th vote for Democrats in the Senate, though two of those are independents. It wasn't clear how quickly the court would rule.
Several of the five justices immediately grilled Friedberg with skeptical questions. Justice Christopher Dietzen said he saw "no evidence or fraud or misconduct."
"It seems like you're offering little more than an opening statement in this case," Dietzen said. "Coleman's theory of the case, but no concrete evidence to back it up."
Friedberg said obvious cases of widely different standards in different parts of the state raise constitutional problems of due process and equal protection.
"When Plymouth has kicked out 75 ballots for signature mismatching and 30 counties kicked out none, we've made our case," Friedberg said.
Justices didn't spare Franken's attorney. Justice Paul Anderson asked Elias if one could find examples of illegally cast ballots included in the count.
Elias said no election passes without some unintentional errors in counting ballots, but said the record in Coleman-Franken includes no evidence that it happened enough to taint the result.
"So you're saying, it was his burden to prove and he didn't prove it, and he can't stand up here now and speculate that it might be wrong?" Justice Lorie Skjerven Gildea asked Elias.
"Yes," he replied.
If Coleman loses, he could petition the U.S. Supreme Court, which isn't certain to take the case.
Coleman and his wife, Laurie, were in the Supreme Court chambers for the arguments. Franken did not attend.