Jeremy may be dumb for a corvid, but he most definitely has their universal attraction to sparklies.
When I was a kid, I always thought the weird images in the "our world began changing" sequence were supposed to be pain-induced hallucinations the rats were experiencing—just abstract nightmare images with no rhyme or reason. It was only after not having seen the movie for several years—and learning more about biology in the meantime—that I realized the twisty ladder-like structures were supposed to be DNA strands being disrupted, mutated...and as they changed, so did the way the rats viewed their world.
The reason Timmy has to be the hero in the sequel is that if Martin was the hero, Timmy wouldn't care enough to do a Face-Heel Turn, breaking the Self-Fulfilling Prophecy. That makes Timmy's hero status EVEN MORE arbitrary.
If the process the rats went through slows the aging process, why does Nicodemus (who was presumably the same age as the others when NIMH took him) look like he's about a hundred years old? Magic (or psychic powers, or whatever) appears to be physically taxing, judging by Mrs. Brisby's exhaustion after using the amulet, and he seems to use it almost constantly.
The two cats survive the elevator falling, despite it audibly crashing a few seconds after Timmy escapes. They then come back to chase him (where they fall down the elevator shaft again). Timmy lampshades this turn of events, that they could come back unharmed after the fall. But the elevator is an explicit ACME product, and while ACME products are always failing in horrific ways they never actually cause long-standing or highly-disabling damage.
The much disavowed sequel to The Secret of NIMH, The Secret of NIMH 2: Timmy to the Rescue has one particularly disturbing Fridge Horror moment. It is when the lab catches fire and the firefighters break open a cage to free several labcoat clad men (presumably scientists) who act and move like dogs. It is not scary as a little kid, but once you know some history, several very unpleasant instances of human experimentation come to mind.
There's also a "Quickthaw" variant of the same scene: Imagine showing up for work in NIMH one day and several other scientists who may have been your colleagues capture and forcibly experiment upon you. When it's all said and done you are left as a canine in a human's body. And it isn't a whole lot better to think they might have volunteered for this experiment.
What if they made you a man in a dog's body?
Another example of a "Freeze-by-Time" one, in which you have to know a bit about animal behavior, is especially terrifying; animals, even domestic species, don't just go to people naturally. You have to condition and imprint and handle these animals, especially at a young age, before they look up to a human as someone to trust. Wild animals will avoid people, even if they have food. Most people think the alley cats from before were just that; stray cats. But, their trust of a human, and their willingness to follow him, can only mean one thing; these were once someone's pets, and they're experimenting on them. Not only that, but the fact that all you see to try to bring in cats was a bowl of food for them, and they weren't wearing gloves in case the cats scratched them, meant that very docile, pet cats, were what they were after. After all, they've been studying mental health, and this has been known for a while.
Remember how terrifying the scene is when Mrs. Brisby tries to drug Dragon? Now imagine it from her perspective: the two she knows have done it have enhanced intelligence over her, but Mr. Ages broke a leg trying it, and Jonathan, her beloved husband, died in the attempt. She's just a mouse... oh, and one whose failure would mean a horrible death for her son, while orphaning her remaining children.
Not just that, but what happened to the rats and mice was based on real-life experiments. They were controversial, but they existed.
More sad than horror, but Jeremy's "Miss Right" is no where to be found in the sequel, nor does she get so much as a mentioning, suggesting the two may no longer be together. She acted as Jeremy's one Bone Throwing in the first film, so it comes off a little saddening for the poor crow.
Why was Jenner so determined to keep the rats from leaving anyway? You could argue that he desperately wanted to rule, but he could've ruled somewhere else too, and he knew NIMH was coming and would likely take him back to a life of imprisonment or death.
The reason Jenner didn't want to leave is because he's strongly against "The Plan" ( the rats leaving the rosebush, abandoning the lifestyle and technology they made there and moving to Thorn Valley). He even killed Nicodemus, thinking it would put a permanent stop to "The Plan." Additionally, he didn't know about NIMH arriving to find them, as Mrs. Brisby was the first to hear about it, and is in denial about her warnings and tries to make her out as a hysterical liar. Add to that Jenner didn't come off as particularly stable a being.
Also, Jenner was willing to fight NIMH. If he had stolen the Stone, it isn't hard to imagine he would have won.
Jenner was many things, but cowardly was definitely not one of them.
The male characters who play a significant role in Mrs. Brisby's ordeal in the film (save for Mr. Ages and Nicodemus) have names starting with "J". Jonathan, her husband. Jeremy the crow. Justin the guard captain. Jenner the Big Bad.