Yeah, there are weak points in armour. It's been taken advantage of, too. I don't know if armour is still like this, but back a while ago (I really don't remember how far back) armour had a weaker chainmail at the bottom of feet, so people could walk properly and run.
There was a war, I really don't remember many details because I learned this years ago, and the opposing side, at least in the beginning of the war, didn't send any troops. Instead, they put sharp metal in the ground that was hard to see. The armour, because it was lacking at the bottom of the feet, was easily pierced by the sharp metal and the troops couldn't cross the terrain.
I don't know how armour is made now, but back then these kinds of weak points were around the elbows, (very slightly) the shoulders, armpits, feet, necks, and so on. However, there's hardly ever armour around necks anyway as the helmet is a separate piece and usually they just make the helmet go lower or have it exposed.
Surprisingly, these weak points were taken advantage of shockingly little except for the common lack of protection around the neck. The neck part is a bit obvious, considering how common it is to know the go for the neck thing. Not only is it vital, it needs to be covered less so your head can be turned around.
I'm not sure about this but I think armour on the shoulders and the top of feet was made of plates sort of, at least one kind of armour did this (although I'm not sure how common it is). It decreased mobility on the feet a bit, but was pretty much fine for the shoulders, The plates could get farther from each other or closer, designed to cover the feet and shoulders even when farther apart and sort of stack when closer. This did however impact mobility, and you couldn't do any clever footwork or bring your arms too far in or out. This made a sort of giant barrier, where no matter how good you were you couldn't really increase your performance because of the limiting armour. I don't think this was used much, and I don't know what it's called but I'm nearly certain it's not plate armour.