Yes, "dog catcher" actually was an elected position, at one time, in some places. But the era in which that was the case appears to have overlapped heavily with the era, our current one, in which the job was a punchline. No one today is actually elected dog catcher; they are simply unable to even be elected dog catcher, as the saying goes. (Which, given that you can't actually run for the position, means that the insult applies to everyone. But we digress.)
This was not always the case.
Slate already disintegrated the idea that people get elected as dogcatcher, in an explanatory post from 2010. "While the unofficial job of dogcatcher has existed for centuries," Christopher Beam wrote, "it was only incorporated into state and local government operations as "animal control" in the 19th century. Since then, the job has almost always been filled by appointment." Almost always.
To wit: S. H. Harper was elected dog catcher in Monessen, Pennsylvania, according to a May 1908 edition of the Daily Independent. The story unfortunately fell at the edge of the ability of the scanning system to read everything, so we may never know what, exactly, Mr. Harper needed to do to prepare for his important job.
A few years earlier, William Missemer won a one-year term as dog catcher in an election reported in the Moberly, Missouri Weekly Monitor. That news report was a sandwiched beneath news of the investigation of the oiling of Emerson Street and an ordinance about a new sewer district. The theme, apparently, was "public utility news."
When Nelson Hobart won unanimous election to as dog catcher in April 1963 in Willowbrook, Kansas, according to the Hutchinson News, he got a different treatment than Mr. Missemer. The important update on his victory warranted not only a headline but also billing above the town's new mayor, council members, and "police judge," which sounds like a bit of a conflict of interest.
Some updates are ... hard to read. For example, there's this update, that ran in Pacific Stars and Stripes.
Is that a joke? Is this some sort of weird military humor about a man with no legs elected dog catcher? Granted, the description that a candidate for a minor office would also be worried about people being out to get him rings true. So who knows.
Then there's poor Maurice Wigderson, who both lost a race for Secretary of State of Wisconsin, but then was forced to endure the ignominy of learning that his candidacy had been compared to that of a dog catcher. (Read through for some great gags on dog catching.)
As we said, the idea of being elected dog catcher was a joke even when people were still being elected dog catcher. The Canyon News apparently used to produce an edition for the local high school. In October 1942, it reported on the results of the eighth grade class elections. Young Harry Campfield won the (presumably honorary) title of dog catcher.
The "can't get elected dog catcher" joke was around even while people were actually being elected as dog catcher. Here's an Associated Press item that ran in the Manitowoc, Wisc. Herald-Times in April, 1967:
So there you go. When you're talking about the guy who couldn't even get elected dog catcher, you're talking about poor Floyd Swan of Almond, Wis.
Update: David Jarman points us to a much more recent election. In March of this year, residents of Duxbury, Vermont, reelected Zeb Towne as dog catcher, over a sole vote of opposition. From Towne's wife.
We weren't able to corroborate the story, but it's so perfect in every way that we had no choice but to include it.