Evil Martin, who's defeated in one blow when Jenny, quite literally throws the book at him; or rather quashes him under a large stack of them, either way.
An even more egregious case with Dr. Valentine, who after so much buildup from Jenny turns out to have been brainwashed to behave like a dog by Martin, without a single punch pulled or even a line of dialogue!
First is Nicodemus' prophecy. It was never mentioned in the first film and was just thrown in for the purpose of giving the film a plot. What's even more jarring is that Nicodemus may have had telekinetic abilities, was wise and had a magical viewing globe but it was never made explicit that he could tell the future. And if he could see the future, shouldn't he have seen that brick coming?
Second is Mrs. Brisby's letter to Timmy that Martin is missing. You would think that because Martin is an important character in the story that this letter should be an important plot point, but it is thrown in quite far into the movie just to explain that Martin went missing. It even looks like Timmy pulled the thing out of his ass.
Timothy finally "learning to listen", after an entire movie of doing exactly the opposite no matter what the situation, when he finally escapes from Martin's prison and begins to actually think through a plan to save his friends. Throwing this claim out as he does comes off as a cheap resolution to the very thing that nearly cost everybody in a big way.
Awesome Music: The reprise of "All I Had is Gone" over the ending credits is perhaps the most moving of all the songs in the movie.
Big-Lipped Alligator Moment: The "Magic Mystery Show", sung by Jeremy and Cecil, accompanied by a bunch of dancing forest animals. It gets really ridiculous at points (Cecil's 'Optimouse' credit card is every bit as nonsensical as a Bat Credit Card,) and after the animals realize it's a scam and chase Jeremy and Cecil away, no one talks about it again.
Gruesome Twosome: First Dr. Valentine and his assistant, and then Floyd and Muriel.
Hilarious in Hindsight: In a meta-sense, the fact so many in the Star Trek: The Next Generation fandom (including his actor) came to hate Wesley Crusher, having Wil Wheaton voice Martin in the original film...and then having Martin become the villain in this one. Although in terms of personality and role in the plot, it's actually Timmy who acts more like Wesley (and is thus hated for it; see The Scrappy).
Idiot Plot: The entire story hinges on the prophecy that Timmy would rise up to defend Thorn Valley in the event that NIMH struck again, and yet it's the rats' utter conviction to this belief that prompts Martin to run away out of jealousy of his brother, which leads to his capture by NIMH and him being brainwashed into the mastermind who would seize control of NIMH and very nearly destroy Thorn Valley. It isn't helped by the fact that Timmy is consistently shown to be too impatient and impulsive to be trusted with the rats' more dangerous undertakings, and in fact it is his own negligence that gets everybody captured the night Evil Martin was prepared to invade the valley.
Evil Martin. Just, Evil Martin in all his hammy glory.
Evil Martin brainwashing the scientists to behave like dogs.
"Dad wasn't crazy!"
Dr. Valentine himself.
The Scrappy: Most of the new characters probably count, but Timmy himself takes the cake for his Failure Hero status, the praise he gets for doing virtually nothing and for his overall recklessness in confronting the obstacles before him.
To give an idea, Mrs. Brisby is in the film for about a grand total of 25 seconds. No recognition is made of the amazing stuff she did towards the end of the first film, not even a "Hey, that was some cool stuff you did." The entire conflict of the movie is an extremely obvious Self-Fulfilling Prophecy that can be seen a mile away, the songs absolutely suck, and almost as if to call attention to the horrible animation, there are a few clips from the first film at the beginning, which actually serve to remind the viewer that "Hey, remember this movie? You should be watching that one again, not this one. See how much better it looks?"
So Bad, It's Good: To some, Evil Martin in general. His being the villain is so bizarre and nonsensical and yet Eric Idle's gloriously hammy performance is one of the (very) few fun moments in the movie. The whole thing (particularly his Villain Song) is so stupid and bad it's hilarious. However, see Base-Breaking Character earlier in this page.
They Wasted a Perfectly Good Plot: Just like how it's mentioned on the trivia page, this movie could've been far better for many if it had adapted more of its elements from Rasco and the Rats of NIMH or having the movie based off of the book instead of what we ended up getting. Strangely despite this, Timmy To the Rescue does share some small similarities with the book.
Unintentionally Unsympathetic: Everybody in Thorn Valley for pressuring Timmy into being like his late father because of the alleged prophecy, even his own family. They spend the better part of several years building up Timothy as the one who would follow in his father's footsteps as the Valley's next great protector before he'd done anything to win such praise. This quickly comes back to bite them all in the butt when he's an adult and eager to prove his worth in this role, only to prove extremely irrational and reckless with his friends having to remind him that "he wasn't ready" for the still-obscure task that lay ahead of him. That said, their earlier praise of him when he was young probably magnified a lot of his bad attitude later in life, remarking that he now acted as if "he knew better than everyone else". It nearly proves fatal not just for Timmy but to the entirety of Thorn Valley, as it is this misguided upbringing that causes them to fall into Evil Martin's clutches.
Timmy, despite all he's built up to be, is made of this, constantly endangering himself and his friends because of his impulsiveness and impatience. In hindsight, he easily does more to endanger Thorn Valley while at NIMH before he can make up for his mistake. Even more egregious is his complete ignorance of what NIMH even is despite knowing of his father's legend in escaping NIMH.
Most of Thorn Valley, who's constant appraisals of Timothy probably lent itself to his arrogance as he got older, and ironically setting off the events that ensured NIMH would strike back.
Martin for running away from home, in spite of NIMH still searching the farm for the escaped rats. He gets himself captured and becomes the brainwashed Big Bad who seeks to bring about Thorn Valley's demise.