My strangest via story was many years ago, sometime in the late 1980s. Several people looked and looked and looked for a small capacitor on a circuit board that no one could find. It was on the schematic, but nowhere to be found on the board.

Then someone found it (no, not me). It was a short piece of bell wire (magnet wire) passing through a via. It was connected on both sides of the board, but the capacitance was between the plated barrel of the via and the wire, with the enamel as dielectric. And sure enough, if you did the math based on the gauge of the wire specified, the final plated diameter of the hole, and the thickness of the board, it actually worked out to be the capacitance reflected on the schematic. (If memory serves, the difference between the dielectric constant of air and something approximate to the dielectric constant of the enamel was in line with the specified tolerance for the "capacitor.")

All in all, it was one of the most creative things I've seen, and about the worst case of documentation I've ever seen.