This is not an answer. Just a very long comment. Mostly I am stunned by the answers given.
(1) First I'm surprised to see Lacan featured as the main example. What I see in these quotes is an attempt to formalise human condition. Is it laughable? Yes! But no more that 16th century physics and widely taken as such. I'm pretty sure 99,9% of the human population never heard of Lacan and was never affected by his thoughts on maths in any way.
(2) If I was in the audience for a talk on "Theorems misapplied to non-mathematical contexts" I'd selfishly like want to see examples that affected me or someone I know. Amazingly, none of the answers given until now mentionned the field of ECONOMICS. Some people in this field are passing political opinions (often political) for mathematical facts every day and this translates into policies that have influence on the lives of millions (if not billions) of people.
Just an example. When the subprime mortgage buble exploded, we heard most banks and insurance companies were shocked because "their experts(*) said the price of houses couldn't go down everywhere in the US at the same time". In fancier terms, it seems that it was widely believed that the use of Collateralized Debt Obligations or CDO's (CDO) and Credit Default Swaps (CDS) were minimizing the risk of default while it was actually just spreading it and increasing it. I am very ignorant in mathematical finance but I'd like someone to try and tell explain to me which theorems that was based on. I'm pretty sure this should go straight to the top of the list.
(*) I used the word "experts" as a generic word for "economists and mathematicians employed by financial institutions".