What was the last election democrats won more counties

[Vosem]

Which means that universal swing to a Ford win probably leaves more counties in Carter's hands than Ford's, making 1976 probably the last time that a neutral map nationally leaves more counties in Democratic hands than Republican ones (though 1980 may also fit this criteria).

What election was the actual last time Democrats won more counties, but Republicans won anyway? One of the McKinley races?

[Vosem]

Should be noted that Horace Greeley was in fact still alive on Election Day 1872. He died between the election and the casting of votes by the Electoral College, which is why his votes ended up scattering (though mostly going to Thomas Hendricks in states he won as a Democrat and to Benjamin Gratz Brown in states he won as a Liberal Republican) rather than the opposition to Grant scrambling to find a new unified oppositionist candidate.