Take Out

No. We take out emotions.

Then, these are bad English?

"He took out his bad day on me."
"He took out his bad game on me."
"He took out his frustrations on me."
"He took out his troubles on me."
"He took out his problems on me."
"He took out his issues on me."

'Frustrations' seems fine. The others if uttered seem casual.

If I read "frustrations" to mean the "things that cause people to feel frustrated", would that change anything?

That is what it means. I fail to see your point.

Then,in:

"to take out [SOMETHING] on somebody"

that "SOMETHING" must be an emotion, but not a thing that causes an emotion?

I don't think it is so neatly definable; I have merely given you my impression.

So, if some had a bad lunch and was angry about it:

"He took out his anger at the bad lunch on his employees."

is good English, but:

"He took out his the bad lunch on his employees."

is bad English?

Yes: it sounds like he threw up on them.

Thanks for your replies, Mr Micawber.

"Frustration" could mean (1) that feeling or (2) a thing that causes that feeling. If I take that second sense and equate "frustration" with "a bad lunch", then I would get:

"He took out his frustration on his employees."

which is okay according to your replies. But,

"He took out his bad lunch on his employees."
is no