Accidentally taught my current cat to sit on my chest when it wants food. Pushing him off and getting up has somehow translated to "she's gonna fill my bowl" in his little mind. I've also accidentally encouraged his yowling when he thinks he's alone because I almost always answer. Great to help him with his separation issues but not great at 3 am.
Few years ago, I had a cat that I taught to jump about halfway up the wall. Using a laser pointer, I used to get it to hit things on the wall. Which eventually led to accidentally teaching it how to "grab" the light switch and turn off the lights. Great party trick until the cat starts doing it by itself cause it wants to.