"Mac Flecknoe" is one of the greatest examples of scatalogical humor you'll ever find and an example of the mock heroic idiom or lofty satire, where the poem is too short to be an epic, which creates tension between the style and the subject matter: one will be high and the other low. Dryden's entire purpose was to embarass Thomas Shadwell, his rival, who considered himself the successor to Ben Johnson. Flecknoe was a poor writer who was also an Irish priest, so the title itself is insulting to Shadwell, as priests can't marry, which makes Mac (Son of ) Flecknoe a bastard poet.
The first line of the poem, "All human things are subject to decay," is an example of heroic sententia. Dryden's stating the obvious, which would elicit a big "D'uh" from modern readers. At the outset Dryden establishes the fact that he's talking about Shadwell taking up the crown of poet laureate from Johnson, with the blessing of his father Flecknoe, both individuals obese -- "And blest with issue of a large increase," and dull -- "who most resembles me." And at line 15 onward we come to the obvious guffaw factor: the "Sh___" references. Of course, the reader is assumed to know it's Shadwell, but the reader also knows the base term for excrement, so making the logical substitution would definitely occur to the reader.
Dryden continues to call Shadwell's writing dull, even to induce a drug-like state: "rising fogs prevail." He further cements the idea of dullness when he says, "Heywood and Shirley were but types of thee," two very prolix (wordy) poets, then uses an image of St. John the Baptist, "coarsely clad in Norwich drugget," to compare Flecknoe's proselytizing to spreading the word of his son's art "To teach the nations in thy greater name."