[Meggy]

Never occurred to me that you were such a nervous person!

On contraire... I'm very calm most of the time

I certainly do agree with you, but there's an "out" left out in the original sentence. Am I right, or am I right?

Yes, you're right, but you needn't have replaced it with another word

The use of definite article is improper in the original phrase. Besides, I think it's much better to simply use the infinitive form of "improve" here. Don't you agree?

I could also say "in order to improve", but it doesn't mean that the previous one was incorrect Both are ok, as far as I'm concerned.

Don't be mad! I have intentionally made that mistake, just to see if you're paying attention!

Bullshit. Paying attention is what I do every single day.
(and "you were paying attention"... right? )

I partially disagree with this one. I admit that "beside that" is quite inappropriate here, but so is "besides"

These two have similar meaning, but not the same... that was my point. "Besides" would be something like "in addition to...", and "beside" means "by" or "next to". Above all, their usage is not the same.