I don't understand your first point, but that could just be the flu talking.
The second point though, I think the opposite is true. You need to understand in your gut that parameters to number-theoretic crypto can be proposed specifically to make your math fail; you need to understand that even if flipping a single bit in your ciphertext garbles the output, that attackers can do useful things with that property; you need to understand that being able to coerce a system into producing the same ciphertext block for the same plaintext block admits terrible attacks; you need to understand where systems "want" randomness versus where they absolutely require it.
It's not enough to know that errors "happen". You have to be able to predict them.
The second point though, I think the opposite is true. You need to understand in your gut that parameters to number-theoretic crypto can be proposed specifically to make your math fail; you need to understand that even if flipping a single bit in your ciphertext garbles the output, that attackers can do useful things with that property; you need to understand that being able to coerce a system into producing the same ciphertext block for the same plaintext block admits terrible attacks; you need to understand where systems "want" randomness versus where they absolutely require it.
It's not enough to know that errors "happen". You have to be able to predict them.