Question: > 
> I noticed that her eyes **had been dancing** as she looked out at the scenery.
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It appeared in a state-sponsored high school leaving examination in Slovakia last week and it seems to have been adapted from a short story by a native speaker, so it really ought to be correct, but I don't see how or why. 

Past continuous seems the obvious choice, this just seems wrong as it's all happening at the same time.

Answer: 
It can be correct but, as with many things in English, it depends upon the context. If the sentence you gave was followed by something like "but now she seemed sad" or a similar alteration in her mood then it would make more sense.
An excellent question, and I think the answer has to do with the fact that this is past report along the lines of indirect speech. (Replace *noticed* with "I thought to myself that ....") Here are two versions in the present tense of the reported noticing, *present progressive*/**simple present**:

> 
> I notice that her eyes *are dancing* as she **looks** out at the scenery.
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The noticing, eye-dancing and scenery-looking are all concomitant, and the tenses cover the same time. When this is reported later, the tenses can be backshifted together, as you suggested, to *past progressive*/**simple past**.

> 
> I noticed that her eyes *were dancing* as she looked out at the scenery.
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But the narrator may notice something at the time that has already passed as he notices. If you'll allow me some non-artistic license:

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> I notice that her eyes *were dancing* as she **looked** out at the scenery and then went dull and lifeless when she turned to look at me.
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Now it's possible to backshift to *past perfect progressive*/**simple past**:

> 
> I noticed that her eyes *had been dancing* as she **looked** out at the scenery.
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The problem here (at least for me) is that the *past perfect* tense generally speaks to time before a fixed **past event**:

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> I *had prayed* for rain before the **storm**.
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Prayer first, followed by a storm. In the given sentence, it's hard to see where to attach the past event. Gazing at the scenery? The *as* clause implies that the eye-dancing and scenery-looking took place together. The noticing? That's a momentary realization (especially when completed in the past tense), and that seems to clash with the progressive verb form, which describes an ongoing situation.