Mundane: From the Latin meaning "worldly," but commonly used to mean "boring."
Aggravate: Means "to make serious," but often used as a synonym for "annoy."
Dilemma: The etymology of the word would restrict its use to having only two unsatisfactory choices, but it is often used to mean a difficult problem, "the dilemma of modern technology."
Incredulous: Means skeptical, but is used as a synonym for "incredible."
"Infer" means to make a conclusion based on facts, and "imply" means to suggest, but these words are commonly used as synonyms.
"Real smart" means "very smart."
"Enormity means "wickedness" but is a common synonym for "immensity."
"Farther" means distance and "further" means additional but these two are historically interchangeable.
"Flaunt" is not a synonym for "flout," but a common phrase is "he flaunted the rules."
"Moot" means debateable, but many use it to mean "not worth debating."