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The main trait of Slytherin house is ambition and cunning.
Malfoy fits the bill. Snape fits the bill. Harry Potter has both, to an extent.
But how can someone argue that Crabbe, Goyle or Millicent (or Pansy if Hermione is to be believed, though she's a bit biased) are intelligent enough to be ambitious (never mind cunning)?
This is a good explanation for all the Sortings that that don't seem to match up with the student's traits. Peter Pettigrew could have been a Gryffindor because he wanted to be brave, not because he was. Although he did develop courage later on, unlike Pettigrew, the same thing could be said for Neville Longbottom. Hermione Granger would have probably been a Ravenclaw based solely on her traits, but apparently she valued bravery more, as evidenced by her telling Harry that friendship and bravery were more important than books and cleverness.
“I’m not as good as you,’ said Harry, very embarrassed, as she let go of him.
‘Me!’ said Hermione. ‘Books! And cleverness! There are more important things – friendship and bravery and – oh Harry – be careful!”
- Harry Potter and the Philosopher's Stone, Chapter 16 (Through the Trapdoor)
There, she basically stated herself that she valued Gryffindor traits over Ravenclaw traits.
Choice also is a part of each Sorting, so if someone wants badly enough to be in a particular House, then they probably will be. Hermione showed a clear preference for Gryffindor over Ravenclaw when she was talking to Ron and Harry on the Hogwarts Express.
“I’ve been asking around and I hope I’m in Gryffindor, it sounds by far the best, I hear Dumbledore himself was one, but I suppose Ravenclaw wouldn’t be too bad …”
- Harry Potter and the Philosopher's Stone, Chapter 6 (The Journey from Platform Nine and Three-Quarters)
There's never been a case where a student is shown to be thoroughly unhappy with their Hogwarts House in the seven books, so it seems likely that the Sorting Hat does place some importance on the student's opinions. There’s also never been a case in the seven books where a student really wants a particular house and is sorted elsewhere.
Over the course of the series, Slytherin is used as the 'evil' House, where everyone bad goes whether they have cunning and ambition or not. Some of them did actually have Slytherin traits - like the Dark Lord himself, who was undeniably both cunning and ambitious. However, others, like Crabbe and Goyle, had none of the defining Slytherin traits. But to fit the idea of Slytherin being the 'evil' House, they were put in Slytherin without any further thought as to why they belonged there other than that they were the bad guys.
That's not entirely true. It's just that the less-bright kids who end up in the other 3 houses try to make up for it somehow, so you don't think of them that way. You think of them as "hard-working", or "diligent". Let's do our own sorting here...
Say you've got a kid who's not too bright, and doesn't like learning for its own sake. We know right off the bat that kid can't go in Ravenclaw. The less-bright kids in Ravenclaw still do pretty well in school, because they enjoy learning new things. It just takes them longer.
Let's further say he isn't inclined toward making up for his lack of talent with hard work, and is a bit self-centered. He doesn't really see much point to taking a tougher path when easier options are available, or to doing things that don't ultimately help himself in any way. Well, we can't really put that kid in Hufflepuff.
Let's further say he isn't particularly brave. For example he will only pick fights with kids that are much smaller than himself, and/or when backed up by superior numbers. Well, he clearly can't be Gryffindor.
But of course none of those things are at all out of place in Slytherin. So all your dumb bullies will naturally end up there. They'll even be welcomed. After all, bullies make great followers for the more devious Slytherin, and together they can all get ahead.
In addition to @Bellatrix's comprehensive answer, inbreeding also plays a role. Most Slytherins are pureblood supremacists and elitists, so they prefer to marry with other pure-bloods from a select few influential families, narrowing their gene pool. While not all Slytherins end up having severely inbred children, their racist and elitist ideology allows/encourages them to go far enough. The Slytherins mentioned in the OP (mentally challenged and/or physically deformed), and also some others like Bellatrix (reckless, extremely ill-tempered and insane), Merope Gaunt (emotionally unstable, has problems with her magical powers and apparently not the most good looking) show some "typically inbred" traits.
https://www.pottermore.com/writing-by-jk-rowling/pure-blood
Increasing numbers of wizards now preached that marriage with a Muggle did not merely risk a possible breach of the new Statute, but that it was shameful, unnatural and would lead to 'contamination' of magical blood.**
[...] ** In fact, the reverse appears to be true. Where families adhered consistently to the practice of marrying within a very small group of fellow witches and wizards, mental and physical instability and weakness seems to result.
Then again:
As Muggle/wizard marriage had been common for centuries, those now self-describing as pure-bloods were unlikely to have any higher proportion of wizarding ancestors than those who did not. To call oneself a pure-blood was more accurately a declaration of political or social intent ('I will not marry a Muggle and I consider Muggle/wizard marriage reprehensible') than a statement of biological fact.
Still, the last quote doesn't necessarily mean that some exceptions don't go more extreme lengths, just that they usually don't or do just enough to keep up appearances.
While just a fanfic, Harry Potter and the Methods of Rationality gave a surprisingly good explanation that I like as headcanon. As we know from canon, the Sorting Hat sorts people based off of not just the quality they most aspire/demonstrate, but also what they personally want, so they don't end up in a house they are unhappy with.
The problem is that Slytherin has become associated with pureblood fanatics and prejudice against Muggles. There are plenty of people that would not want to be associated with this sort of bigotry. It's also known as an "evil" house, prone to birthing dark wizards, which people also wouldn't be happy with. Thus some who may otherwise demonstrate cunning and ambition end up being sorted into other houses. They disagree so much with the other traits Slytherin has become associated with that they would be unhappy being in the House.
Of course, canon suggests that the number of students in each house has to be kept roughly equal. Thus the Hat may be forced to take people who don't fit into the level of "cunning:, but who don't mind being associated with pureblood rhetoric, just to keep the numbers similar to that of the other houses.
If you have a clear idea on where you want to go, you go to that house.
Until Cursed Child came along, we never saw anybody unhappy with their sorting.
I think that we need to consider the extent to which HP is part of the sizeable genre of "British Public School" (= private school in most other cultures) literature. And the fact that in most such institutions, you will generally be placed in the house to which your parent who attended that school belonged - probably all the way back to your 7xgreat-grandparent! Crabbe Snr and Goyle Snr are Death-eaters
I think it's simply not the case that "less bright students end up in Slytherin". Probably all houses have their share. Witness: Neville ... Hufflepuff. You just don't notice them because (a) they are supported (as others have said) and (b) only evil stupid students make it into the plot line.
(I also vaguely recall some less-bright students in Divination classes, though can't quite remember who or what house, but not Slytherin).
On Pottermore this is part of the welcome to Slytherin house message:
Because you know what Salazar Slytherin looked for in his chosen students? The seeds of greatness. You’ve been chosen by this house because you’ve got the potential to be great, in the true sense of the word. All right, you might see a couple of people hanging around the common room whom you might not think are destined for anything special. Well, keep that to yourself. If the Sorting Hat put them in here, there’s something great about them, and don’t you forget it.
And I think that is something to keep in mind in any world; there is much more to everything than it might seem esp at first glance. There are reasons you shouldn't judge a book by its cover or by its name. The same goes here. Just because someone doesn't act on some trait (or doesn't have some trait) doesn't mean they don't have it (or can't eventually develop it).
Something else is this: Rowling wrote about how the Hat is obstinate it is never wrong but then you have:
The Sorting Hat is notorious for refusing to admit it has made a mistake in its sorting of a student. On those occasions when Slytherins behave altruistically or selflessly, when Ravenclaws flunk all their exams, when Hufflepuffs prove lazy yet academically gifted and when Gryffindors exhibit cowardice, the Hat steadfastly backs its original decision. On balance, however, the Hat has made remarkably few errors of judgement over the many centuries it has been at work.
But nothing is perfect in our world and nothing is perfect in the world of Harry Potter (perhaps exactly because our world is imperfect).
Finally, Dumbledore says to Severus that he sometimes thinks they sort too soon. After all, Severus was very brave too. But there it is: he also had qualities of Slytherin, didn't he? Dumbledore says this about Harry also. Similarly Hermione turned out to be brave and the Hat considered .. was it Ravenclaw (? I'm pretty sure that's the one) .. for her. And look at Neville; he didn't believe in himself but he turned out incredibly brave. We all have hidden talents and other kinds of traits we don't know about or don't fully realise or develop to full potential. I know this is very true of myself as I've proven to myself (and friends/family insisted) in some things and friends/family insist to me about other things.
To put it another way: we all have many positive and negative traits as well as neutral traits (if you can call any trait 'neutral' as I can). Does any one trait or even any five traits necessarily define that person? Only to those who are biased; anyone being realistic and accepting the possibility will see that there is much more to everything in this world perhaps people esp.
Pottemore also has another article on this very subject which I by chance noticed a few minutes ago: https://www.pottermore.com/features/why-being-sorted-is-not-as-simple-as-it-seems
They also bring up the concept of a Hatstall which is another thing to consider: it really isn't as simple as the traits they look for. It's not black and white.
