The Family Way (Original Motion Picture Soundtrack), composed after the Beatles stopped touring in 1966 and the first time Paul's music wasn't credited to Lennon/McCartney, but he split the profits with John, anyway (1967)
Thrillington, a big band-flavored orchestral version of Ram credited to the pseudonymous Percy "Thrills" Thrillington (1977)
Liverpool Sound Collage, an ambient electronica album also credited to Youth, Super Furry Animals, and, because it samples Studio Chatter and stray instrumentation from a few of their recording sessions, The Beatles (2000)
Twin Freaks, a collaborative album with The Freelance Hellraiser that heavily remixes songs from Paul's catalogue (2005)
Abbey Road Crossing: The cover of the concert album Paul Is Live features an older Paul digitally inserted into the original, iconic Abbey Road cover photo.
Adorkable: At least when he's making mashed potatoes 
Album Title Drop: "She sprinkles flowers in the dirt, that's when a thrill becomes a hurt", from the song "That Day Is Done".
There's a partial one in the song "Fine Line": "There is a long way between chaos and creation" (the album in question being Chaos and Creation in the Backyard).
Alternate Reality Episode: Three albums released under the name "The Fireman", a "group" consisting of Paul and the record producer Youth. The first two albums were sound collages. Electric Arguments, still rough and unpolished but a more conventional collection of songs, got strong reviews.
There was also his and Linda's 1971 (but not released until 1977 due to other obligations) Thrillington project (an orchestral album consisting of covers of Paul's entire Ram album), credited to the pseudonym Percy "Thrills" Thrillington.
Analogy Backfire: The analogy of piano keys representing racial harmony in "Ebony and Ivory" falls apart when you try playing a C and a C-sharp at the same time. Musical notes that sit side-by-side on the keyboard do not get along, regardless of colour.
Divorce Assets Conflict: Part of the extremely ugly end to his second marriage, with model Heather Mills. Mills got a large sum that was still less than a fifth of what she wanted, along with the judge's assessment that she was "less than candid".
"Non nobis solum "Sed toti mundo "Nati "Toti mundo nati"
Greatest Hits Album: He's had several. Wings Greatest covers mainly Wings, but has some early solo tracks. All the Best is under Paul's name, but is about half Wings. The two-disc Wingspan is the most comprehensive collection, covering both Wings and Paul's solo output through 1984.
Also, "Little Willow", written in memory of Maureen Starkey (Ringo Starr's first wife).
Happily Married: Paul and Linda McCartney for 29 years, until Linda's death from cancer in 1998.
I Am the Band: "Paul McCartney and Wings". To the extent that the greatest hits album All the Best is attributed solely to McCartney despite being about half-Wings.
On McCartney, McCartney II, and Chaos and Creation in the Back Yard, Paul performs almost all the instruments himself.
Iconic Item: His trademark violin-shaped Höfner 500/1 bass.
Intentionally Awkward Title: Kisses on the Bottom. It's a line from "I'm Gonna Sit Right Down and Write Myself a Letter," and in that context clearly refers to signing love letters with X's, but still... Paul...
Older Than They Look: He's 70, but he looks like he's in his late-40's to mid-50's. One reason for this is that his hair used to be greyer than it is now.
Parental Substitute: Julian Lennon has admitted that he was much closer to Paul than his own father, especially during his early childhood and adolescence. When John deserted Julian and his mother, Paul stepped in as a role model and even wrote the song "Hey, Jude'' to console a young Julian over his parents' divorce.
“Paul and I used to hang about quite a bit—more than Dad and I did. We had a great friendship going and there seems to be far more pictures of me and Paul playing together at that age than there are pictures of me and my dad.” - Julian Lennon
Prison: McCartney's infamous bust in 1980, when, as he and Wings were arriving in Japan on a tour, he was caught at customs with 218 grams of marijuana in his luggage. He spent ten days in jail and could have faced a seven-year sentence, but the Japanese government elected to deport him. Reports of John's reaction to the bust range from "delighted with his ex-partner's misfortune to the point where he literally danced with joy" to "furious that his friend let himself get caught and increasingly anxious as Paul was detained"; at any rate, he called to provide moral support.
Real-Life Relative: Among the persons "knocking at the door" in "Let 'Em In" are "Sister Suzy" (a nickname for Linda), "Brother John" (Linda's brother), "Brother Michael" (Paul's brother) and "Auntie Gin" (Paul's aunt).
Refuge in Audacity: Despite having full knowledge that it would be banned by the BBC (which it was), "Give Ireland Back to the Irish" was released as a single by Wings. Their first single..
Rooftop Concert: Naturally, played with the other three Beatles in the band's final performance on the roof of Apple Corps, but Paul has also done it solo, having played on the marquee of the Ed Sullivan Theater on The Late Show with David Letterman.
Self-Titled Album: McCartney (his solo debut, in which he belatedly announced the breakup of the Beatles) and the later McCartney II.
Supergroup: Performed a new original song called "Cut Me Some Slack" with the surviving members of Nirvana for the "12 12 12" benefit concert. It rocked.
Take That: "Too Many People" off of Ram is a rather veiled Take That towards John Lennon. The photo on the inside sleeve of Ram—a beetle...er, screwing another beetle—is less veiled, though Paul intended it as a reference to the acrimonious collapse of the Beatles instead of specifically insulting John. Lennon, always more willing to get nasty than McCartney, took his revenge with "How Do You Sleep?".
Word of God is that only the line "too many people preaching practices" was about John and Yoko. John thought the whole album was about them.
While the common misconception is this, McCartney's reason for being angry at Jackson seemed to change from MJ "buying the rug he was standing on," to some of the choices he made in exploitation of the songs (e.g. putting certain Beatles songs in certain commercials) to simply not giving McCartney—one of the wealthiest men in showbiz—a raise in the royalties.
Paul and Linda's relationship with Denny Laine of Wings didn't end well, either, although Paul and Denny seen to have reconciled.
And, of course, Paul's relationships with the other Beatles melted down rather spectacularly in the late 1960s. They all later managed to patch up their differences to some degree following that, but there was reportedly never the same closeness.
Wig, Dress, Accent: During Beatlemania he took to wearing disguises so that he could wander the streets without being mobbed (and occasionally play pranks on the other Beatles and Brian Epstein). In one amusing incident, he was recognized by a bartender who wasn't fooled when Paul asked for "a drop o' the hard stuff" in an Irish accent. See also Paul and Linda incognito at a George Harrison concert.
Word Salad Lyrics: Paul was fond of these; "Junior's Farm" and "Jet" are two prime examples.