Crossword puzzles flex one very specific piece of cognition--the ability to find words, which is also known as fluency. Fluency is a type of process based in the speech and language centers of the brain. So doing crosswords might help you get better at word finding, but that's the sum total of their positive benefits to your brain.
misnomer. n. 1. an incorrect or unsuitable name or term for a person or thing. 2. the act of referring to a person by the wrong name.
A word that everyone else is afraid to define except in utter seriousness, for fear of being branded a rascist, in total ignorance of the colloquial usage of the word, its characterization in popular culture, and the populations of people it is used most by.