"Subject + Be" vs. "Subject + Being"

Question

1. I don't see things will improve anytime soon.
2. I don't see things improving anytime soon.
3. I don't see things are improving anytime soon.
4. I don't see things are going to improve anytime soon.

So I'm wondering which one of those above is correct? (From my understanding, 2 sounds nature the most)

I came up with the question when I came across this sentence on a forum:

"I probably should have mentioned it being a terrible idea"

The thing is, I can't find any differences between it and this:

"I probably should have mentioned it was a terrible idea"

I find this really confusing, when to use "Subject + Be" or "Subject + Being", such as:

"I didn't remember the traffic was this bad" VS. "I didn't remember the traffic being this bad"

Answer 1

Of your four sentences, 2) and 4) are fine.

But it is not exactly analogous to the sentences in your details. Those latter sentences had "being" vs. some other form of the verb "to be" while your first four sentences had forms of the verb "to improve".

On your first four, whether 1) and 3) are correct or 2) and 4) are depends on the verb that proceeds them. In your case, with "see" you want either 2) or 4) but if you substituted "think" for "see" then 1) and 3) would be right and 2) and 4) would be wrong.

Answer 2

Being means it's happening right now while was means it happened in the past.

Though with the word "this" makes both seem to point to "now" even if they're not.