Learn English – Best word for health problems

This article by Wikipedia (reformatted) discusses the choice between noun adjunct and attributive adjective (when the choice is available):

Use of noun adjuncts when an adjectivally inflected alternative is available.

It is a trait of natural language that there is often more than one way to say something. Any of the options that is logically valid will usually find some currency in natural usage. Thus "erythrocyte maturation" and "erythrocytic maturation" can both be heard, the first using a noun adjunct and the second using an adjectival inflection.

(1) In some cases one of the equivalent forms has greater idiomaticness; thus "cell cycle" is more commonly used than "cellular cycle".

(2a)In some cases, each form tends to adhere to a certain sense; thus "face mask" is the normal term in hockey, and "facial mask" is heard more often in spa treatments. Although "spine cord" is not an idiomatic alternative to "spinal cord", in (2b) other cases, the options are arbitrarily interchangeable with negligible idiomatic difference; thus "spine injury" and "spinal injury" coexist and are equivalent from any practical viewpoint, as are "meniscus transplant" and "meniscal transplant".

Regarding the latter class, attempts at extensive editorial prescription are usually past the point of diminishing returns; ensuring local consistency is sensible (e.g., avoiding random intradocument juxtaposition of both forms for the same meaning), but trying to enforce absolute interdocument consistency (e.g., to never stet a noun adjunct if an adjectival inflection is interchangeable) would only illustrate that indeed, "A foolish consistency is the hobgoblin of little minds, adored by little statesmen and philosophers and divines."

So, since both 'industry problems' and 'industrial problems' are commonly used (as can be seen on the internet), do they have distinct senses ((2a) above) or are they closely synonymous ((2b))?

While I'd agree with mok that '"industry problems" ... put[s] the stress on the area in which the problems have occur[r]ed', ie a specific industry, I'd say that "industrial problems" can be used here also, but should be the choice for more general situations (eg a general strike).

Saying

What is the best time for a meeting?

does not prevent the listener from interpreting it so that more than one time is suggested.

However, saying

What are the best times for a meeting?

further emphasises giving more than one time.

Both are correct and mean what you want to mean.