Ninety-nine episodes
Mac turns Gilligan's Island ending at 99 episodes into a conspiracy and pulls Charlie into finding an explanation.
Supporting source ↗CASE FILE · S18 E07

Mac and Charlie drink the proverbial Kool-Aid while trying to uncover the mystery of why "Gilligan's Island" never made it to 100 episodes.
THE SHORT VERSION · SPOILERS AHEAD
Mac turns Gilligan's Island ending at 99 episodes into a conspiracy and pulls Charlie into finding an explanation.
Supporting source ↗While Frank has the gang destroy old paperwork and repaint the bar, Mac and Charlie read ordinary details as evidence of a cover-up.
Supporting source ↗Mac and Charlie picture the gang in Gilligan's Island roles, then treat a fake pigeon camera and Cricket's window spraying as proof they are being managed.
Supporting source ↗The gang pitches a 100th episode to a man they mistake for Sherwood Schwartz's grandson; he explains that his identically named grandfather owned a Laundromat in Albany.
Supporting source ↗THE EVIDENCE
Charlie joins Mac's Gilligan's Island investigation and destroys Frank's paperwork with boiling Kool-Aid.Source ↗
Dee is folded into Mac and Charlie's imagined Gilligan's Island scenario and the later pitch.Source ↗
Dennis helps stage the gang's imagined Gilligan's Island scenario and joins the later pitch.Source ↗
Frank assigns document destruction and exterior painting, then joins the pitch to the falsely identified heir.Source ↗
Mac turns Gilligan's Island's 99-episode run into a conspiracy and helps pitch a supposed Schwartz heir.Source ↗
Cricket is paid by Frank to keep spraying the windows, making Mac and Charlie mistake the rain effect for part of a conspiracy.Source ↗
Mac and Charlie discuss Gilligan's Island while boiling and staining Frank's documents in Charlie's apartment.Source ↗
Frank has Dennis and Dee repaint the exterior while he directs Charlie and Mac to destroy old paperwork.Source ↗
A fake pigeon with a camera and the gang's pre-existing hidden cameras feed Mac and Charlie's surveillance theory.Source ↗
Frank directs Charlie and Mac to destroy annual paperwork; they boil and stain it instead of shredding it.Source ↗
The episode transcript identifies an instrumental of Sweet Georgia Brown during the Harlem Globetrotters reenactment.Source ↗
The episode transcript identifies Temptation Sensation during the opening transition.Source ↗
Mac and Charlie investigate why Gilligan's Island stopped at 99 episodes and mistake a Laundromat owner's grandson for Sherwood Schwartz's heir.Source ↗
Tags document researched occurrences, not every appearance. Read the research notes and attribution.