One of the advantages of writing a mystery series is the fun (and it is fun) of sharing "inside information" with readers of the series. By that I mean references that the author makes in some books to events and characters in others. For regular readers, the author is saying: "You know what I mean, don't you? Remember when that happened?"
Agatha Christie "winks at" regular readers quite frequently that way. For instance, in Cat Among the Pigeons, Julia Upjohn, a student at the exclusive Meadowbank School, refers to "Aunt Maureen" Summerhayes, a friend of her mother's, mentioning that she makes, "a smashing omelette." Maureen Summerhayes is the owner of Long Meadows, a notoriously badly-run Guest House in which Poirot stays in Mrs. McGinty's Dead. What's amusing about this reference is that in Mrs. McGinty's Dead, it's clear that Maureen Summerhayes is a terrible cook who doesn't think "it matters much what one eats." In the end, Poirot teaches her to make a good omelette, and mentions that fact to Julia Upjohn. Regular readers, of course, understand the reference right away and can laugh at it.
Christie does the same thing in Hallowe'en Party. In that novel, Ariadne Oliver, Christie's fictional author, is helping to organize a Hallowe'en party for young teenagers. When a young girl is murdered at the party, Oliver asks Poirot for help. As they discuss the case, Poirot asks if Oliver was there to organize a Murder Hunt - a scavenger hunt for clues to a fake "murder." Oliver answers, "never again!" That's a reference to Dead Man's Folly, in which a Murder Hunt that Oliver does organize has disastrous results.
Sometimes, Christie includes "spoilers" in her stories. In Cards on the Table, there's a distinct spoiler for one of Christie's mysteries. In Poirot Loses a Client (AKA Dumb Witness), Christie mentions the names of the murderers in three of her other novels.
Christie, of course, isn't the only author who "winks" at readers. In Ten Days' Wonder, Ellery Queen returns to Wrightsville, the same small town in which he solves the case in Calamity Town. Queen mentions his first "Wrightsville case" in Ten Days' Wonder, and refers to both cases in The King is Dead.
Lilian Jackson Braun frequently refers to earlier cases in her later novels. Many times, she does this by having characters from earlier novels reaappear in later cases. For instance, in The Cat Who Came to Breakfast, Jim Qwilleran, Braun's sleuth, meets Elizabeth Applehardt, the eccentric daughter of a wealthy family. Elizabeth later moves to Pickax, the scene of many of the Cat Who.... mysteries, and, among her other enterprises, becomes the owner of the Grist Mill Inn, as readers find out in The Cat Who Dropped a Bombshell. We find out she also owns a boutique in The Cat Who Sang for the Birds. Rita Mae Brown does the same thing in her Mrs. Murphy series. For instance, in Wish You Were Here, Kelly Craycroft, a rich paving contractor, is among the victims of several murders that occur in and near Crozet, Virginia. His widow, Olivia "Boom-Boom" Craycroft, appears in many of the later Mrs. Murphy mysteries. She refers often to her loss, and her complicated relationship with Mary Minor "Harry" Haristeen, Brown's sleuth, runs throughout the series.
"Inside information" can keep regular readers interested; it is, in a way, a "thank you" to readers for their loyalty. However, as with most aspects of a mystery novel, it's a double-edged sword. The best mysteries also do well as standalone novels, so that readers can enjoy them whether or not they've read any of the other novels in a series. So we mystery novelists have to give enough detail about the "inside information" that new readers can follow the plot. As I work on my own Joel Williams series, I'm including a few references to other novels as they come up. I don't think "inside information" should be forced, though. Like other aspects of good writing, it's best when it comes naturally.
What kind of "inside information" do you get from your favorite series' authors? Do you think those hints at other novels add to or detract from a mystery?