This will probably not be considered a serious mistake, but maybe it counts:

According to Dray, Manogue if you ask the following question to scientist:

Suppose the temperature on a rectangular slab of metal is given by $T(x,y)=k(x^2+y^2)$ where $k$ is a constant.

What is $T(r,\theta)$?

A: $T(r,\theta)=kr^2$
B: $T(r,\theta)=k(r^2+\theta^2)$
C: Neither

most mathematicians choose B while most other scientists choose A.

(I don't know if this experiment was ever done on a large scale. I do know some people who studied mathematics and have tried to argue that A is the right answer.)

This question is called Corinne's Shibolleth in this article of Redish and Kuo, where it is discussed further.