It seems unlikely that either of these Bush v. Gore arguments would fare well in court. To begin with, there's a great debate over whether Bush v. Gore even has precedential value (the opinion contains unusual language limiting its application to "present circumstances") and, assuming it does have value, what the case means. Reading the ruling narrowly to require application of equal standards for ballots counted in state-mandated recounts, Coleman should lose. The problems Coleman points to with the alleged counting of certain illegal absentee ballots occurred before the recount; both the canvassing board and the court in the election contest appear to have achieved great uniformity in the treatment of similar problematic ballots. And certainly nothing in Bush v. Gore requires the counting of ballots that don't actually comply with the election statutes. If anything, counting such ballots could raise equal-protection problems. And since we cannot identify which illegal absentee ballots were cast for which candidate, we can't just take those out from the vote totals in the name of promoting equal protection.
Coleman's Bush v. Gore arguments depend on the most generous readings of the equal-protection principles of Bush v. Gore, which say that courts should find an equal-protection violation when there are systematic deviations across a state in how similar ballots are treated. Most courts have so far rejected such arguments. For example, both the 6th and 9th Circuits have rejected lower court rulings holding that it violates Bush v. Gore to use unreliable punch-card voting machines in some parts of a state rather than others.
Even if a court were to accept this generous reading of Bush v. Gore in the abstract, its application to Coleman is problematic. As Ned Foley explains, under Coleman's theory, if Coleman could find a jurisdiction in Minnesota that allowed felons to vote (contrary to state law), the court would have to count illegal votes cast by felons throughout the state. In essence, Coleman is asking the courts to compound equal-protection problems in the state by adding more illegal votes to the total.
Perhaps Coleman's lawyers would respond that Bush v. Gore then requires a new election because of errors of local election officials in administering a statewide election. But the logical end point of that argument requires states to take over from local election authorities the business of administering elections under uniform standards. This isn't a bad result, I'd argue, but one that that courts would be loath to adopt. It would open up just about every close election to a redo, because problems with election administration are endemic in the United States, with no guarantee that the redo will get the job done any better.
In the end, Coleman doesn't have a strong equal-protection argument. Then again, most of us thought George W. Bush didn't, either.