Is there a word or concise phrase for this type of question?

Some questions appear clear, but are deceptively difficult to define, and their answer is very sensitive to the exact technical definition of the question, in such a way that it renders the original question almost meaningless.

What would you call such a question?

Examples

How many islands are there in Denmark?

According to wikipedia (http://en.wikipedia.org/wiki/Denmark#Geography_of_Denmark), there are 72 inhabited islands, 443 named islands, and 1419 islands above 100 square meters. However, it does not list how many islands there are in total, since it is so hard to define what constitutes an island. Some islands would be extremely small, and others tidal. Islands are created and destroyed by geothermal activity so you would have to specify a time or take it as the time of asking. Also, sometimes a peninsula (e.g. Jutland) may be considered an island if it is separated from the mainland by rivers.

How many words are there in English?

It depends on which dictionary you look at

What proportion of the laws of the United Kingdom are made in the European Union?

This was a subject of an article on the BBC's Radio 4 programme 'More or less'. It is difficult to define what is a law, since there are statutory instruments and various regulations that may or may not be counted. Also, some laws implement European Union law, others just refer to it. I believe the program said the total could be between 7-50%, depending on your definition.

Solution 1:

If the answer to the question depends on how someone chooses to define the terms used in the question, and the choice of definition is not obvious, clear, or widely-agreed-upon, then I would say that the question is ill-defined (or "poorly defined", if you prefer).

Solution 2:

If the question is worded in such a way that the reader does not know what is being asked, because the syntax of the sentence can be interpreted in more than one way, then the question is "vague".

This question is clear in the sense that it is only asking for the number of islands in Denmark, and not for anything else:

How many islands are there in Denmark?

However, this question contains "non-specific terminology" or "includes vague terms" because the definition of "island" depends on whether the island is large enough to be considered an island. Parts of the question "need clarification".

In the question "How many words are there in English?" the word "English" is a non-specific term, because whether or not a word is recognized as being a word varies according to the exact variant of English used, E.G. Modern English.

However, because the word "word" could include or not include slang that might not be considered a word, you could argue the question is vague because it contains multiple non-specific terms: "English" and "word".