A typical Porter move—you can hear it in "Begin the Beguine" and "I Love Paris"—is to start a song in a low register and then push the line ever upward until it has an almost Wagnerian intensity.
(This was a trick that was picked up by Porter's friend Irving Berlin, who used it with success in songs like the Porter-esque "Let Yourself Go.")
One thing I'd take issue with is the statement that Porter "never had to broaden his stylistic scope." It's true that Porter always stuck to certain kinds of songs and shows (his show Mexican Hayride, written in 1944, was an old-fashioned, unstructured, slapdash musical comedy at a time when everybody else was scrambling to imitate Oklahoma!). You can always predict the types of songs you'll find in a Cole Porter score: the list song with topical references, the Latin-flavored love song, and so on. He didn't overhaul his style the way Kern did in the '20s or Rodgers in the '40s.
But Porter, more than most Broadway songwriters, modified his style to fit the changing fashions in popular music. In this he was different from, say, Jerome Kern, who disliked a lot of the changes in pop music and declined to acknowledge them in his music. (In 1924 Kern spoke out against jazz, which he felt showed disrespect for the composer by arranging his tunes beyond recognition. Rodgers and Hart actually wrote an anti-jazz song in 1939, called "I Like to Recognize the Tune.") Porter, who was sort of an outsider to Broadway and became successful by consciously figuring out how to write the kind of songs that the public wanted, always made sure to adapt his songwriting to the prevailing taste. He introduced Latin rhythms into his songs in the '30s in recognition of the fact that this kind of music was catching on; instead of scoffing at jazz, he paid tribute to it in songs like "Red, Hot and Blue." During World War II he wrote big band-flavored music and deliberately simplified (some might say dumbed-down) the references in his lyrics, again to suit the then-prevailing fashions. A Porter score is a time capsule; give him something like the Good Neighbor Policy, and he'll write a "dance sensation" song about it (Mexican Hayride):
A super step
Is the Good-Will Movement,
It's in that pep
But with this improvement,
It's got that rum-tum
Here's to ya, chum,
Salud, amigo, salud.
Only Irving Berlin was as responsive to changes in popular music as Porter was, and I don't think it's a complete coincidence that both Berlin and Porter started to lose their footing in popular music in the mid-'50s, when there was no more consensus on the "prevailing" style in pop music.
As a lyricist, Porter's specialty was the internal rhyme (rhymes within a line, as opposed to at the end of lines). One of his favourite tricks, which almost no one did before Porter started doing it, was to rhyme consecutive words within a line, which, in Stephen Sondheim's description, "makes [a] line rock solid" and emphasizes the rhythmic profile of the music. Examples:
Get the sweet beat of the organ sealing our doom
If you know of such a spot, not too far from town
("Pick Me Up and Lay Me Down")
That dopey, mopey menace
("We Open in Venice")