These are what we call the 'YMMV items.' Things that some people find in this work. We call them 'your mileage might vary' because not everyone sees these things in the same way. This starts discussions in the trope lists, a thing we don't want. Please use the discussion page if you'd like to discuss any of these items.
Critical Research Failure: "Tom and Jerry meet Sherlock Holmes" gets a pretty noticeable case of this if you happen to be a Sherlock Holmes fan. In one scene, Holmes mentions the case of the Red-Headed League and Watson responds that it was a crime perpetrated by Holmes' nemesis, Moriarity. The Red-Headed League caper was actually masterminded by a criminal named John Clay.
Might be a genius bonus - at least one Holmes adaptation (the Jeremy Brett series) has retconned Clay into being an underling of Moriarty.
"Rock'n Rodent" really should've been called "Jazzin' Jerry"; the music in the cartoon sounded closer to upbeat jazz than what rock & roll sounded like when the cartoon was released in 1967.
"Mouse in Manhattan" uses "Manhattan Serenade" for the bulk of the picture, and it has to be the most brass-heavy, upbeat version of the song ever composed.
As far as the Deitch shorts go, his final cartoon "Carmen Get It" is light-years ahead of any of his prior shorts in the soundtrack department, swapping out the sparse, tinny music previously used for a decent-sized orchestra and some actually very good renditions of the music from Carmen.
Nowhere is this worse than in "The Two Mouseketeers", which Tom's death is somehow treated as heroic despite Tom not doing anything heinoius and Jerry and Nibbles showing no remorse for him.
In fairness, the number of times Jerry lost his Karmic Protection and ended the short defeated or in a stalemate with Tom are deceptively large.
Designated Villain: By the same token, we're almost never meant to be rooting for Tom, even if he didn't actually do anything to provoke Jerry (or if Jerry doesn't even have the right to be provoked, like in the short when he screws with Tom's opera recital because it was disturbing his sleep; nevermind that Jerry's the idiot who decided to set up shop in a concert hall. Other 'genius' places he's decided to set up shop include inside a piano and inside a pool table.).
Dork Age: The Gene Deitch shorts, which wreck the formula by giving Tom a Jerkass owner who beats the stuffing out of him whenever he slips up. Moreover, it suffered a lot of animation errors. Not to mention the 1980s TV shorts.
It's arguably meant to act as Truth in Television. Jerry is a mouse and thus takes whatever food is available to survive, making him more of a Loveable Rogue. Though granted there are shorts where he steals a bit more than his own means.
Human: Besides, a mouse doesn't eat very much...
*Jerry glances at a huge pile of stolen food hidden in his mousehole*
"Blue Cat Blues" more or less seems to suggest that suicide is the best solution to a lousy love life, as Jerry's inner monologue laments, "It's better this way."
Franchise Original Sin: Tom and Jerry would in some of the original shorts be friends and speak, though rarely (and something would always come between their friendship, making them fight again). These elements are what is most reviled about The Tom And Jerry Show from the 1970's, and Tom and Jerry: The Movie.
Fridge Brilliance: In the Sherlock Holmes movie, Red being so into the wolf seems odd. Then you realize she's most likely not intended to be the Red of the original Red Hot Riding Hood... but her Grandma in her youth, who is crazy for Wolfie.
The earliest cartoons featured Tom and Jerry looking more like a real cat and mouse, and making real animal sounds. Hanna and Barbera soon realized that this made them too much like laughing at animals getting hurt, and anthropomorphized them a little more.
For some this even applies to Gene Deitch's shorts, as quite a few fans felt that "Carmen Get It" was where Deitch and the animators finally managed to nail the Tom and Jerry formula. Unfortunately for Deitch, that was the last short he worked on for the series; MGM pulled the plug on his team and gave the series to Chuck Jones immediately afterwards.
Internet Backdraft: When news came of the release of Tom and Jerry Golden Collection Vol. 2 deliberately not including the long awaited shorts "Mouse Cleaning" and "Casanova Cat", Warner Home Video got hit with such rapid online backlash from fans and collectors (amazon.com's page for the set has 105 one star reviews, all complaining about this) that they decided to postpone its release (although its uncertain if it will get released with the shorts, or will be canned altogether).
Jerkass Woobie: Both characters fall in this trope rather sadly. Jerry, for exemple, may be exceedingly vindictive on Tom, but he generally is only trying to survive, and be honest, Tom generally deserves what comes upon him. Tom, on the other hand, is often punished for his own cruelty towards Jerry, usually ironically, but there times were he becomes the victim of Jerry without provocation, and as said before, Jerry can go away too far in his retalation at times. Also, Tom tends to be threated like crap by several other characters (like his owners and Spike) for little to no reason, and for the most times, Tom chases Jerry away because he's ordered so, rather than any actual malice towards the mouse. So, he doesn't deserved all the shit that happens to him.
The Problem with Licensed Games: The SNES game is just another bland platformer, where the player, as Jerry, plays through a series of stages, running around until he hits the end of each stage and fights Tom. Along the way, he can pick up peas that he can use to throw at his enemies. The music is composed of nothing but random beeps. The game's multiplayer aspect is no better; to quote a YouTube commentator:
So, lemme get this straight, both players, not even playing at the same time, have to complete the level, and if one dies they switch.
Ron the Death Eater: Tom never ever did anything wrong! Tom was only following his instincts, how dare Jerry object to being eaten!
Draco in Leather Pants: Jerry is a cute lovable mouse! It doesn't matter if he ruins Tom's life again, again, and again! It doesn't matter if he steals food and other things from the houses owners! That dirty tomcat deserves all the abuse he gets!
This actually made it's way in universe to some extent. Allegedly Hanna and Barbera got several letters from fans rather irked by the heavy punishment Tom suffered in many early short. As a result many more later shorts actually let Tom get the last laugh (most of which were karmic victories due to Jerry starting the feud).
Suspiciously Similar Song: The direct-to-video films (such as "Tom & Jerry & The Magic Ring") feature a sound-alike to the classic Tom & Jerry theme.
In the case of "The Karate Guard", not only does the opening horn fanfare sound similar to the ones in the classic cartoons, but Warner Bros. designed their Vanity Plate to look very identical to MGM's blue-background cartoon intro.
Squick: Heavenly Puss, as mentioned above (the implied causes of death of the cats in line for the train - most particularly the kittens in a burlap sack).