I have been listening to Dan Carlin's podcast about the mongols (Wrath of the Khans) and it's really getting quite silly. It's like a novel written by a 10 year old (not the way Dan tells the story, but more about what the story is about). "And the mongols were the BEST at this, and the BEST at that, and they had spies and engineers and horses and were the fastest and then one time in this battle they got outnumbered 20 to 1 but they won anyway because they're the best" - i am exaggerating but you get the point. They are described as being vastly better than any enemy they face and there's -nothing- that can stop them.
Did the mongols have any weakness?
Well, they were indeed the best army before guns were invented. Their military campaigns sound like fairy tales. But they didn't write their own histories. So it is more believable than the Greek histories which were written by Greeks.
Of course they had weaknesses. They had no experience in naval war (Japan). Also jungle was a very difficult terrain for them and they were bad at hot and humid weather (Vietnam).