Black Sheep Hit: A lot of people seem to think of the Police as an '80s pop band because of Synchronicity, but it was actually quite a departure from the majority of their albums. (Granted, it does make up 20% of their collection). The distinctive Police sound was really an accelerated reggae rift that they called "white reggae" (hence the name of their second album).
Also, Ghost in the Machine was for the most part very funk-influenced, but notably the exceptions were the radio singles ("Spirits in the Material World", for all the synthtrickery, is essentially a reggae tune, "Every Little Thing She Does Is Magic", Stewart's reliably forceful drumming aside, is a pop song, "Invisible Sun" is an ominous droney dirge).
Creative Differences: They disbanded in 1986 after Sting and Stewart Copeland couldn't agree on which drum machine to use.
That was just the "straw that broke the camel's back" according to Copeland. The band had already almost broken up while recording Synchronicity (which they actually had to record with the three of them in separate rooms) and Sting had a solo career going on.
Specific pre-breakup example: Andy and Stewart weren't impressed when Sting showed them "Next to You", feeling that its lyrics weren't aggressive or political enough, and suggested replacements. Sting refused to change anything. Stewart was also dismissive of the Blues Rock slide guitar solo, calling it "old wave".
Creator Backlash: Sting says that he'd throw about half of Zenyattą in the trash, and the other bandmembers agree that the album's quality suffered from a rushed production (it was finished on the day that their world tour started). Andy said he became disenchanted with their direction around Ghost, when the "fantastic raw-trio stuff" got drowned out by all the horns and synths, and "we ended up backing a singer doing his pop songs".
Producer Nigel Gray thought the title of "Behind My Camel" was a sign of Andy undergoing this:
He didn't tell me this himself but I'm 98% sure the reason is this: what would you find behind a camel? A monumental pile of shit.
Hipgnosis: Did the cover art for the British "De Do Do Do De Da Da Da" picture sleeve.
The Pete Best: Henri Padovani was the band's first guitarist. He only got to record the first single ("Fall Out"/"Nothing Achieving", in 1977) before being replaced by Andy Summers. Even then, he only played the guitar solos on those tracks, as Stewart Copeland, the songwriter, felt Padovani wasn't up to the task, and so Copeland played lead guitar on them.
Throw It In: Sting accidentally sat on a piano and laughed during the recording of "Roxanne". The group liked it so much they left it in there. Also, Stewart Copeland can make any song awesome with his improvised flourishes.
"Does Everyone Stare" begins with Stewart Copeland's original demo for the song, where during recording his microphone picked up a freak radio signal that was broadcasting opera. The resulting opera bit was left in the song because it happened to be in the same key.
"Be My Girl - Sally" is more or less the product of this, stapling together a fragment of a song Sting hadn't finished, and Andy's silly spoken-word poem about the joys of having a sex doll.
What Could Have Been: Sting recorded 13 demos and only 6 made it to Ghost In The Machine. The 6 originals that didn't make it were pretty awesome. One question — why hasn't he properly released them later?
When the trio got back together in 1986 for one last-ditch attempt at recording, Stewart Copeland broke his collarbone in a horse-riding accident the day before and couldn't play the drums. Summers admitted that they lost the opportunity to dampen hostility by just jamming around, and they ended up disbanding for good.
The band almost re-recorded Fall Out for Reggatta De Blanc. It would have been interesting if that version had been released, since Andy Summers' guitar style is much different to Stewart Copeland's (Henry Padovani was the band's third member at the time of Fall Out, but only played the solos).