Alliteration, punning, and rhyming are a trio of tried-and-true techniques for letting your prose out of the pen, introducing levity (perhaps at the expense of brevity). When inadvertently applied, however, they can distract readers because their use is inconsistent with a writer’s tone, or because the application is excessive. Here are some comments about proper and improper use of these writers’ tools.
I enjoy reading and writing alliterative prose. When overused, alliteration can backfire, because it might lead readers to focus on the messenger rather than on the message. In moderation, however, it is a proven strategy for entertaining while informing. But it is rarely appropriate for formal writing or when a serious tone is required, so be careful not to introduce it on purpose or by accident in such contexts, such as in the statement “There are multiple methods for maintaining mortality records.”
Away from the keyboard, I’m an unrepentant punster, but because punning is the most intrusive of these three techniques, I generally avoid it in writing; even in light-hearted content, it can be obtrusive. Beware unintended punning in such remarks as “If we were in his shoes, we’d sell our souls for the opportunity,” where readers might read souls as soles.
A related, and more fraught, problem is carelessness about accidental double entendres. I’ll leave specifics to your imagination, but any review of one’s writing should include vigilant attention to the possible presence of words or phrases with risqué connotations.
Deliberate rhyming in prose is less common than employing alliteration or puns, though it’s appropriate in specialized cases such as mimicking Dr. Seuss in order to emphasize the absurdity of a phenomenon. But take care not to release sober but accidentally silly written remarks like “In the weeks before the election, pundits had a predilection for overemphasizing the offhand remark.