''InspectorSpacetime'' has accumulated numerous {{Noodle Incident}}s, as the protagonist is a time-travelling [[ExoticDetective alien investigator]] whom even his close associates only know by a job title. In the new series, Noodle Incidents have become a RunningGag.
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! The Classic Series:
* The details of the Inspector's mysterious overarching mission from the Infinity Knight High Command are referred to only obliquely, even in their appearances in "The Crime Sports", "Return to the Sphere of Strands ", "The Lethal Murderer", and the "Internal Investigation of the Inspector" arc.
* We don't know why the Sergeant turned to a life of crime when he and the Inspector apparently started out as [[BuddyCopShow colleagues]].
* The Doctor frequently alludes to future crimes and criminals in Earth's timeline, such as the Great Brain Robbery, Mac the Nipper, the Trey Clones, and assorted interplanetary gang wars.

! The New Series:
* The Time Wave that destroyed Kayaclasch and ([[JokerImmunity supposedly]]) the Blorgons in the new series is the most prominent example. Lots of maddeningly cryptic hints have been dropped about who did what to whom when and where, from such strange events as the Rise of Hy-Brasil and the Inundation of Ys[[note]] neither of which had ever been mentioned, much less visited, in the classic series[[/note]] to the heavy implication that the Inspector himself was framed for the destruction Kayaclasch. Of course, we've never seen what ''actually'' occurred, though "The Last Minutes" throws in a few {{Red Herring}}s.

!! Ninth Inspector:
* From "Explodingville": "I told you we should have turned right!"

!! Tenth Inspector:
* "The Chaucer Puzzle" ends with one: Following the arrest of the highwaymen who robbed Chaucer, a fat drunken knight shows up, recognises the Inspector, declares that he is his "bosom friend", and promises to pay back the money he owes him. As the Inspector hasn't met him (yet) he has no idea what was going to happen. "The Last Minutes" clarifies this a bit: Apparently, his old drinking chum is [[spoiler: Sir John Oldcastle, the historical inspiration for {{Creator/William Shakespeare}}'s [[Theatre/HenryIVPart1 Falstaff]]]].

!! Eleventh Inspector:
* "Fangs in Florence":
-->'''The Inspector:''' That's a nuisance, 1580. [[Creator/NiccoloMachiavelli Machiavelli]] was born a hundred and eleven years ago. Wanted to look him up. He owes me a chicken.
-->'''Aiden:''' Machiavelli owes you a chicken?
-->'''The Inspector:''' *briskly* Long story, I gave him a recipe.