Monk has been around for quite some time, over the episodes he has learned many different things. Let's name them, I'll start off with one from pilot.

Floss is strong enough to hold up a man's arm.

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Flash causes retinal scarring!
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In Psychic, he learnes a small pebble is the size of a ---small pebble.

You can't clean Nature with Nature.

In the kid he learns how to change a diaper.

He has learned that he can carry his own package of wipes in his pocket. (from Natalie?)

He has learned that there are many people who love and care about him.

"Takes his Medicine"

"The Monk" learned how to play Marco Polo.

He learned that happiness doesn't come in a pill

And that happiness doesn't come from seeing Santa on the roof of an asylum.

He learned that cleaning the keyboard could lead him into lots of trouble.

I believe he has learned that it is possible for him to love a woman besides Trudy, although he probably wouldn't let himself until he solves Trudy's murder.

Be suspicious of policemen with boomboxes and dollar bills hanging from their belts

He learned that he can't trust guys who play card games for money (on the Manhattan one).

In "Mr. Monk Goes Home" he learned that he really does love his brother.(Awwwwww ...) He also learned that Ambrose and his father both feel as guilty about the father leaving as he does.

And he learned that if you eat a candy bar eleven months after its expiration date, you'll get an awful tummyache

He learned that foot wine (forgot the name of that wine) was what him and Trudy always drank on their anniversary.