The filing argues that the election result is in doubt because there are too many rejected ballots that are still uncounted. "Many of these ballots come from precincts that voted predominantly for Coleman, as the MSCB's [Minnesota State Canvassing Board] tallies show, making clear the failure to count them affected the election's outcome." Here the Coleman camp seems to be quite openly admitting that cherry-picking has been involved in finding ballots -- something everyone knew, but nobody would affirm -- and using it as an affirmative argument.
The brief also says that the trial court "badly skewed Coleman's burden of proof" by requiring strict compliance with absentee ballot laws for admitting any new ballots in, and created a standard different from what Coleman alleges was the real overall practice of mere "substantial compliance" used by local election officials on Election Day.
Interestingly, the filing quotes from a previous Supreme Court ruling that it says bolsters its case against "violations such as those resulting here," from local officials' disparities in administering the state's uniform statutory standard. Team Coleman quotes the U.S. Supremes saying "the weight of a citizen's vote cannot be made to depend on where he lives." However, this case is in fact Reynolds v. Sims from 1964 -- a redistricting case for one-person-one-vote, not an elections administration case.
As for Coleman's meaning of "substantial compliance," the preferred burden of proof for letting in new ballots, the briefing lays out a series of positive presumptions that would apparently let nearly any ballot in: That a ballot's requirements of registration, or application, or witnessing, etc, should be presumed to be satisfactory absent immediate evidence otherwise. It's hard to imagine this working out.
There is, however, an exception to the principle of greater enfranchisement: Team Coleman argues that the Election Night results must be rejected for a Minneapolis precinct that lost an envelope containing an estimated 132 ballots in the recount, which would have the effect of taking away 46 net votes from Al Franken. The argument here is that in a manual recount, these are "votes not 'legally cast.'"
That said, Coleman has staked his case on a single, more or less consistent claim to count more votes that are presumed to have been cast for himself. We'll see what happens.