There are literary terms for certain types of mispronunciation, but, as far as I know, no literary term that covers all of them.
- The spoonerism is probably the best-known example. For example, "The Lord is a shoving leopard" instead of "The Lord is a loving shepherd." From a linguistic point of view, a spoonerims is a type of metathesis.
- An eggcorn "is an idiosyncratic substitution of a word or phrase for a word or words that sound similar or identical in the speaker's dialect". Examples: "ex-patriot" instead of "expatriate"; "on the spurt of the moment" instead of "on the spur of the moment". Strictly speaking, eggcorn is a linguistic term rather than a literarary term.
- Of course, you can use homophones for comic purposes. A famous example of this occurs in the Four Candles sketch by The Two Ronnies. In this sketch, a customer in a hardware shop pronounces "fork handles" as "fork 'andles", so the shopkeeper misunderstands it as "four candles". When the customer asks "O's / ose (?)", the shopkeeper successively interprets this as "hoe(s)", "(garden) hose" and "(panty)hose", after which the customer finally explains he wants "letter O's". The omission of the letter 'h' (combined with a lack of clarification) increases the potential of misinterpretation because it leads to more homophones.
From a psychological or psycholinguistic point of view, the most relevant term may be paraphasia: "a type of language output error commonly associated with aphasia, and characterized by the production of unintended syllables, words, or phrases during the effort to speak" (Wikipedia). Obviously, this is outside of the realm of literature or comedy.
Outside of the pathological domain, there are several types of speech errors that are relevant, e.g. those classified as anticipation ("leading list" instead of "reading list"), blends, deletion, morpheme exchange errors and perseveration (e.g. "black bloxes" instead of "black boxes"). These, too, are outside of the realm of literature or comedy.