Welcome to English Forums, Zach! It is a puzzle, isn't it? First, the prepositional phrase ("of pesky critters and rodents ") should not be confused with the subject of the sentence.
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Zach BoyerAnd if I changed the word to "herd" instead of "group," would everything you said still apply?Yes, but a herd is seldom thought of as individual members, as in "herd mentality."
AlpheccaStarsThe subject is "group" which is a collective noun, like "company", "team" or "family."American English treats these nouns as singular (there are exceptions, though).Hmmm, I remember learning in these hallowed halls (from GG, I believe) that notional concord applied particularly to "group" in AmE.
Zach BoyerOK, you're right, forget herd. What about "horde," though? That would still use "comes," right? Thanks! —ZachHorde is so rare, that there is no convention.
Zach Boyer"What is really interesting is the way this horde of pesky critters and rodents comes within range of …"That's fine.