I wouldn't be doing that, I think you should be looking at....

[sunshineoutdoors]

As opposed to
I wouldn't do that, I think you should look at....

Is it ok to talk like this? Sometimes I find myself saying "be xxxxing" instead of just "xxxx" and it annoys me a bit because it doesn't seem right, but when I think about it I can't actually put my finger on what's wrong with it.

Is it just a clumsy way of talking? Or is it a grammatical crime? Or is it in fact the correct way of expressing oneself in particular situations and I'm just unclear about the rules?

Does anyone know? Or indeed, care?

Is it maybe a regional thing? I would never say "I wouldn't be doing..." and nor have I heard anyone else say it.

Really? What about "I don't think you should be doing that?"
I'm in Yorkshire, I never thought it might be a regional thing, I'm sure I've heard other people speaking like this, admittedly also in Yorkshire.

This thread is making me nostalgic for Harry Enfield

Is it grammatically incorrect though?

I have the feeling that your second example ("I don't think you should be doing that") is not a real example of what you are trying to convey. Though to honest I'm a bit confused myself, so I am about to propose a detour into a similar, though I think related, form of sentence construction.

In Ireland, it is common to say (for example) "I'm after forgetting my coat". This sentence construction actually comes Irish but has been carried over into English and adopted as common usage. I think that what you're trying to highlight might be something similar.

Not sure though. I definitely use this type of construction and never really thought it was wrong or uncommon...