Related to the mondegreen is the eggcorn: a phrase that is a substitution of one word or phrase for a similar sounding word or phrase - like when people think that Alzheimer's disease is really called old-timer's disease. Or that to a T is really to the teeth. The term eggcorn is an eggcorn for acorn, according to NPR.
Then, of course, there are malapropisms, which are instances in which a speaker mistakenly uses a word in place of another, similar sounding word. The name comes from mal a prop, according to Wikipedia, a french term for inappropriate, but came into wide use because of a character called Mrs. Malaprop in the 1775 play The Rivals. She said things like "Illiterate him quite from your memory." My all-time favorite malapropism comes from good old Dan Quail, who once said "Republicans understand the importance of bondage between a mother and child." And they say Democrats promote sexual deviancy.
I scream, you scream, we all scream for ice cream uses an oronym - a type of word play in which the speaker uses two phrases that sound exactly alike but mean different things. These expressions are prime fodder for dad jokes - like the story about the hungry man who went to the beach to eat the sand, which is there (sandwiches there).
Spoonerisms are expressions in which the beginning sounds of two words are swapped - bass akwards, nucking futs. The term spoonerism came about in the early 20th century, after an Oxford lecturer called William Archibald Spooner, who was prone making them accidentally. Spooner was in no way amused by this.