The Commonwealth Court panel quizzed lawyers for the party and its Republican-backed challengers, with a decision expected Thursday.
With nearly 13,000 signatures still contested in a petition challenge now in its fourth week, the party is barely 2,000 signatures shy of the 20,601 it needs to qualify for the ballot.
The challengers want to disqualify 11,000 signatures for deficiencies such as listing an address that doesn't match the voter's registration or omitting the year from the date of their signature. If successful, both sides agree it could prevent the party from qualifying.
The Libertarians' lawyer argued that about 3,000 of the signatures set aside for wrong addresses should be allowed under the 1993 National Voter Registration Act because they involve voters who moved within the same county.
The lawyer, Paul Rossi, also questioned the need to include the year on a form that was printed in 2012 for an election that will be held in 2012.
"It's all a game of mirrors intended to keep the minor parties off the ballot," he said.
Ronald Hicks, representing the challengers, said case law has firmly established that state law applies to nominating petitions and that it requires signers' addresses to match their registrations.
Workers hired by the party to gather petition signatures did "a sloppy job," he said.
The Libertarians' presidential nominee, former New Mexico Gov. Gary Johnson, is listed on the ballot along with the party's candidates for other statewide offices that include U.S. Senate and state attorney general.
The Green Party's presidential candidate, Massachusetts physician Jill Stein, qualified for the Pennsylvania ballot and no challenges were filed. The Constitution Party also sought to qualify its presidential candidate, but gave up amid a GOP-backed challenge.