In Guards! Guards!, Vimes appears to have no idea that he is related to a noble family. Plot Hole or was it not part of his character yet? (I've only read the Watch books, so...)
I doubt Terry Pratchett had planned the history of Stoneface Vimes etc when he wrote Guards! Guards! Even so, it's not really a Plot Hole. The Vimes family haven't been nobles for several hundred years. Remind the GG-era Vimes that his great-great-great-great-grandfather was a nobleman who lost his rank for killing the king, and he'd just say "Yeah? So what?"
There's a time delay between GG and MAA (where he appears aware of the connection, at least during his conversation with Carrot just after the explosion at the Assassins' Guild), so possibly he did a bit of reading up in the interim.
Even in Men At Arms, Vimes doesn't seem to know much about his family history. It's Carrot who's read up on it, and discusses it with Vetinari who refers to Stoneface Vimes having been the head of the watch at the time of the regicide. Vimes knows about the regicide but doesn't know his own connection to it. It would be after Men At Arms and his marriage that he researched the subject, or heard about it from Carrot or elsewhere. Presumably Sybil would know more about it than he initially does, too.
A very brief reference in Night Watch suggests that Vimes never knew his father, and that his mother told him his dad was run over by a cart when he was small. (It's also implied that this was a lie, indicating that Vimes Sr. either died a much nastier death or abandoned his family.) If Vimes never knew his dad, it's only logical that he wouldn't know much about his father's family, at least until Carrot's remarks spurred him to look into it.
I always interpreted that line to mean Sam Vimes was a bastard and his mum didn't want to explain that to her son.#
Oh. Vimes is a bastard no doubt about it. Dunno if he's illegitimate or not...
We know from Dragon King of Arms' recitation of his lineage that "Vimes" was his father's surname. Presumably, Vimes' father had at least a common-law relationship with his mother for a time, else she'd probably have given her son her surname instead.
Connectedly, Vimes voices no strong opinions in the monarchy/republicanism debates that the story raises. It's Colon of all people who has the anti-monarchist rants. So even if Vimes knows about his Cromwellian ancestor at this point he doesn't seem to feel sympathy for his cause yet. Characterisation Marches On, I guess.
It has always bugged me that Sam "This is how you play Lawful Good" Vimes is willing to accept all the various interesting ways it is possible to commit "suicide" in Ankh-Morpork. Like going into a dwarf bar and ordering a "short beer," etc. etc. While that makes for a clever one-off joke, what it basically means is that Sam Vimes' City Watch deliberately turns a blind eye to MURDER on a regular basis. Calling it "suicide" takes all the blame off of the murderers and all the responsibility off the Watch to do something about it. And that's not the attitude of the Lawful Good, that's the attitude of a Dirty Coward.
It's probably nothing more sinister than the sort of dark humour that people in jobs such as police work tend to get due to the job they do being pretty grim at times. The series never actually says they dismiss these cases as less than murder, just that these cases are called suicides in a darkly humourous way, plus there are scenes of these and/or similar situations (pub brawls for example) in plenty of the books where the attackers ARE arrested.
Also, given the crime rate in the city at this point in the series, if the Watch stopped to investigate every such murder, they'd never get anything done. Probably also because "Being a Watchman questioning people in the Drum" also counts as suicide.
And remember, this is Vimes before he became Vimes. This is the pathetic, drunken Vimes who does want to do the right thing but doesn't have Carrot's good influence to make him bloody well stick to that. At this point in Ankh-Morpork history, the entire (three-man) Night Watch is a joke. It's hard for a joke to seriously investigate any crime.
Vimes believes in protecting the innocent, presumably he doesn't extend the definition of innocent to what we would call trolling (although if you called it that in Ankh-Morpork then you'd almost certainly just have committed suicide). Remember they have a "Being Bloody Stupid" law, so they are almost certainly breaking that, how fortunate that breaking it is also its own punishment. As long as it is done off the streets then the peace has been kept.
And in the early books, Vimes probably felt there were few if any real innocent people in the city at all.
No 'probably' about it. Remember (in a book I can't remember offhand) where he prevents Detritus firing the Piecemaker because he might hit an innocent person, "Even in Ankh-Morpork."
There's also the possibility that the city in which the 'Being Bloody Stupid' act is actually enshrined into law also has decided that asking a Troll if he has rocks in his head is legally regarded as suicide.
Look at it from Vetinari's point of view, someone who has gone to lengths to cause problems and raise ethnic (speciesist?) tensions has now through his own stupidity caused his own removal from both the city and the gene-pool, and in a way that handily highlights the problems such behaviour causes. Provided the property damage is kept to a minimum then it doesn't effect the city, except by removing an irritant from it.
And then again, there's the undeniable fact that despite the gallows humor, living with this state of affairs is one of the many things that is slowly killing Vimes. I don't think it's a coincidence that his recovery from alcoholism and his growing power to actually protect the innocent instead of just talking about it happen at the same time.
How do you lock an overthrown dictator in a dungeon without noticing that the locks aren't on your side?
The lock is on the outside of the dungeon (or more accurately both sides), it's the various bolts and such that are on the inside.
Putting someone in a dungeon isn't like a hotel, where the guard would walk them around and show them the amenities and then open the door to leave... they open the door, insert the prisoner, and close the door, never seeing the inside of it.