I get what you say, but being unusual shouldn't be the mark of being a 'freak'. Freaks, as we know them, are a very specific group, and regular mobsters may or may not label everyone who's just slightly different from them as a 'freak', but that shouldn't be the standard. I was trying to figure out how would the film's audience see the Penguin, not how would other mobsters see him.
The definition of freak includes the word "unusual". I think it's inherent to being a freak. The way audiences see them in comparison to the norm is what measures their "freakitude". I suspect most people would consider Oswald Cobblepot (whose very name denotes him as different) to be quite apart from the "norm".
I think the "slightly different than normal" is actually sort of a valid measure. It begs the question...are they truly that unusual, or just extensions of normal concepts?
Is Cobblepot deformed? Not that I'm aware of, not in all interpretations. He had flippers instead of fingers in Dark Victory and Long Halloween, but I always believed that was just Tim Sale honoring the DeVito look, they didn't really mention any deformity to his characters. Being short, fat, ugly and bald and having a big nose is not really a deformity.
In most portrayals, he has a massive, massive nose. It goes beyond "big". I don't know that this would translate well to a serious version, but...a larger than average nose is sort of a must for the character. Granted, I think you can satisfy "freak" without having the person be deformed. You could say he's somewhat "deformed" mentally, though.
Well, in War Games Cobblepot was not even deformed, if I remember well. And his clothing is not unusual, just unusual to certain circles: the mob.
Where I live and where I've been, most people don't dress only in tuxes constantly, or wear monacles, or tophats almost everywhere they go. Even the very, very wealthy. Cobblepot's manner and often, his style, of dress is eccentric and a pervision of societal norms and ideas about high society.
Being too elegant is not something that sets him apart from everybody.
Ah, but being obsessed with it is, wouldn't you say?
He doesn't identify with a color, or with a symbol, or with anything else. He just likes two unusual things: to carry 'gadgety' umbrellas around (I'm not too fond of the over-protective mother explanation) and birds, which really is not that strange.
I suppose it depends on the faithfulness of the portrayal. But a mature, fairly intelligent mobster who is obsessed with birds on any level, or who uses trick umbrellas on any level, is not the norm today.
He's not really a freak. That would be like Gotham's policemen believing that Gordon is a 'freak' just because he is friendly towards the Batman and has a big bat-light on the roof.
Gordon has been considered such before, I'm sure. He was something of an outcast in the department simply for being a good cop, at one point. And going up to the roof to meet with a psycho vigilante isn't exactly normal.

. In most towns, at least.
No, because he's seen as a freak by regular mobsters, competitors, who would always try to find ways to taint his reputation within the crime-world. Besides, there are other factors too: his own opinion about himself and how the real 'freaks' see him. Dot they see him as part of the or just too moderate and old-fashioned? It's a good thing to consider too.
The Penguin, despite his desire to be "normal", still wants to be seen as different. He's a narcissist. It's one of the interesting incongruities of his character.
I'm sure the freaks see him as one of them. That's how it's been portrayed for decades. The Penguin is one of the Big Three: Joker, Dent, and Penguin.
Really? Why? Imagine a mob thug with two big scars in the shape of a smile, just like the Joker.. but nothing more than the scars. No weird personality, no weird world-views, no lack of past, the scars were made to him by someone else. No scars, and he's just your typical run-of-the-mill gangster. Is he a freak? No. Let's say he always dresses in white. White shirts, white trousers, whie shoes, white suits... a signature look. Let's say his name is John Smith, and his fellow mobsters call him "Pure" Johnny Rotten.
Does that sound to you like a freak? It shouldn't. Unnatractive physical appearance and high taste in clothing doesn't make a 'freak'. Certainly not by 'definition'.
No, but neither should a faithful version of Cobblepot be a man with a slightly large nose and no odd psychological compulsions. You start adding things in like an obsession with birds and umbrellas and the biggest words he can find...and "Johnny Rotten" gets a little freakier, I'd think.
That is like saying that Batman is marked by the campy spirit that preceeded the modern "darker" versions. We're talking about films here, not the comics, but even then, is the Penguin a freak in the comics? Isn't he sane? Doesn't he never go to Arkham because of his sanity? What makes him
different from... say, Lex Luthor?
No, I'm saying that even in the actual world of the comics...it is accepted that The Penguin spent time as a "freak" before he became a mob boss. He has a reputation he cannot quite escape.
The Penguin and Luthor share some similarities, sure. They're both "businessmen". But whereas the comic continuity has Luthor just always being a businessman (sort of, it varies from year to year it seems), The Penguin evolved from a true freak into someone who wants to be more, but who still has the same elements he had as a freak. Because he simply usually cannot help himself with these elements. Birds. Umbrellas. Big words. Going "Waughhh, waughhh, waughhh" on occasion.

.
Define "watering down". I'm not even sure what image of the Penguin you have in your head.
Watering down is the removal of his key elements. Burton's Penguin was almost the reverse, because Burton took Penguin's key elements and turned them upside down. A watered down Penguin would be an Oswald Cobblepot with no psychological compulsions, no image issues, and no penchant for umbrellas, large words, etc. Are those things somewhat gimmicky? Could he survive as a character, even a good character, without them? Absolutely. But it would be a watered down version.
It depends greatly on the interpretation. I don't recall the Penguin ever being in Arkham, but maybe you can refresh me (and that it's not sarcasm).
Someone else beat me to it. He's been there before. Usually in some sort of "I caught you, you're going to Arkham" capacity, mostly in the 80's (in the late seventies, oddly enough, he usually went to Blackgate). We've seen him in the cells as Batman walks past, TLH's Penguin was an Arkham dweller, I believe, and so have several other versions been. It's generally accepted that as things currently stand in the comics, though he was once a freak in fine form, he's escaped his "freak past" to a point, and is considered mostly sane.
In BATMAN BEGINS, Arkham Asylum was used as a place to keep thugs out of real jail time, but it clearly was populated by the insane as well. I question whether half the people sent there are truly insane, but that's another discussion.
That is what I was trying to do. I was asking what did 'freak villain' means to other people. As I said before, to me, it all comes down to insanity, and I believe that the Penguin should be insane. Neither just a 'regular mobster'. If we were going to have a man that's in the safe middle ground between the mob and the super-freak-villains, that should be him.
You believe The Penguin should be insane? Or shouldn't be. I agree about the middle ground. But I think he's got to be someone who took what he was, and evolved from that, in an attempt to, as he's always tried to do, better his station, and to be more than he truly is.