So, you know what your favorite color is? Not everyone's that clever.

Happy birthday to the ground!!!

I would say its humour is very nuanced and has a range of type, and need not be categorized as intelligent though I'll make my case for that below.
Certainly at times the dialogue is verbose and occasionally clever, but more often trys to sound smart without actually being so. However, in the context of the scenes it still achieves the desired comical effect. Its employment is therefore a wise choice.
For instance the French Soldier near the beginning of the film goes on talking in a non-sensical way, while Arthur is trying to have a meaningful conversation. The humor is in the friction between a character who is absurd and a character who wants to be taken seriously. Its not the most scintillating, but intelligent people will certain appreciate the irony.
Another example of a similar situation would be Arthur's encounter with a peasant. Again the peasant is unexpectedly verbose and thwarts Arthur's intentions of establishing himself as king, but where this scene is slightly more intelligent than the first is in the content of the exchange. The peasant starts lecturing about civics which satirizes the social order of the period. The peasant tries to use big words (for him anyway) making him sound pseudo-intellectual, but we've all been to parties with people like that which I think makes it even funnier. While the irony is similar, this time its the fault of Arthur who's perrogative is benign but is demonstratably immoral based on the enlightened ideas of proper governance that emerged in the subsequent millenia from when this film takes place. I don't think the juxtaposition of ideas regarding monarchies and democracies, rights to rule, etc. would be humorous at all to a person who didn't readily understand those types of things.
Anyway I could go on and on making conjectures about how this film is intelligent and what not, but at the end of the day I think we can agree on two things: one - that the humor of this film will appeal to more nerdy, dorky people, and two - that those people tend to be more interested in the things other than money, fashion, sports, celebrities, etc. that most people don't really care about, which I would argue is a characteristic that correlates with intelligence.

It was never silly. The Colonel always put a stop to anything that became silly. - JustAMessageBoardPoster2
Or a knight (or knnn-iii-gggg-ittt) who would bop you over the head with a rubber chicken. Or a 16-ton weight that would drop onto you. . . .
"We hear very little, and we understand even less." - Refugee in Casablanca

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Partly right you are OP.
I am British myself, and would wholly agree that Monty Python as a whole is silly. It is however surreal in places and the jokes are not all cheap sex gags nor jokes relying heavenly on saying a certain "f" word like say a vast majority of Hollywood comedies nowadays.
"Have you ever tried to grab a tongue?" ~ Karl Pilkington

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So, this is childish humor, but Mr. Bean is funny? That's a joke right?

Agree with you, the movie is childish and amateur, using imaginary horses was too pathetic. I rate it 3. And it's not that I don't understand British comedies. Mr bean is very funny for example. And also some other TV series I don't remember their names.

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It does involve "silly" humor like the cows being flung but it also does have intelligent humor. The entire scene with Arthur and Dennis could be seen as "intelligent" humor, I mean if you have no idea what "anarcho-syndicalist commune" means, then you won't find the scene funny, and that's that. I mean, at the end of the day, I think that the movie is hilarious and I honestly don't care whether someone disagrees.