The story
Verschlimmbessern is a German verb made by fusing two others: verschlimmern, to make worse, and verbessern, to improve. The result means to make something worse through an honest attempt to make it better. The German dictionary DWDS credits the coinage to Georg Christoph Lichtenberg, the Göttingen physicist and aphorist, in the second half of the eighteenth century. The noun, Verschlimmbesserung, followed in the nineteenth.
The word is informal but respectable. German newspapers use it about politics, for instance when hasty repairs left an electoral law in a worse state than before. It has a second, narrower sense too: to edit a text and spoil it, the copy-editor's own version of the problem. A blunter synonym is kaputtreparieren, to repair something to death.
What makes it hard to put into English is the good intention built into it. Botch and bungle blame skill, and backfire blames fate. English also has the rare word disimprove, which names the result but not the effort. Verschlimmbessern keeps the effort in view: someone meant well and left things worse.
A scene: a Saturday morning, a dripping kitchen tap in Leipzig. A man fetches a spanner, decides the washer needs replacing, and in the process cracks the valve. By noon the water is off for the whole flat and an emergency plumber is on the way, at weekend rates. His wife looks at the puddle and says one word: 'Verschlimmbessert.'