Sometimes you get two at once. Here's a double play, from speech quoted by Cornelia Dean in "Physicists in Congress Calculate Their Influence", NYT Science Times, 6/10/08, p. D2:
Problems arise not just in obviously science-related issues, but also, as Mr. Holt [congressman Rush Holt] put it, in "those countless issues, and it really is countless, that have scientific and technological components but the issues are not seen as science issues."
Stripping away some extraneous complexities, we get:
(1) Problems arise in countless issues that have scientific components but the issues are not seen as science issues.
There is a parsing of (1) in which it's unproblematic, but I think the parsing Holt most likely intended has a gapless relative in non-parallel coordination (two phenomena we've written about here before, but not in combination).
The unproblematic parsing has (1), as a whole, as a coordination of two clauses, connected by but:
(2) [Problems arise in countless issues that have scientific components]
[but the issues are not seen as science issues].
The conjunction but in (2) contrasts the arising of problems with the view of various issues as not scientific; this is possible, but somewhat odd. More significantly, the part about problems arising is Dean's wording, while the part about the viewing of issues as not scientific is a direct quote from Holt. So I suggest that Holt intended the clause introduced by but to be the second conjunct in the relative clause modifying countless issues:
(3) [that [ ___ have scientific components]
[but the issues are not seen as science issues] ]
The first conjunct in (3) has a gap in it (in the position of the subject), as in standard English relative clauses, but the second conjunct is gapless (with the issues in subject position); gapless relatives aren't standard English, but they are not infrequent, especially in speech (see discussion here). In any case, the two conjuncts in (3) aren't parallel in form.
Non-parallel coordinations, of many different types, have been a favorite topic here on Language Log since the early days. As far as I can tell, we haven't looked at this particular type — coordination of a gapped and gapless relative — before, and I don't have examples of it in my files, but I suspect it's not uncommon; things like (3) are so easily comprehensible that they probably escape notice. (It is, unfortunately, very difficult to search for them.)
In my earlier posting on gapless relatives (linked to above), I distinguished three types — two with a "resumptive pronoun" in them and one (NoPro) with neither a gap nor a resumptive pronoun. There are some stunning NoPro examples, like this one cited by Mark Liberman a while back:
How can we provide a service that the consumer goes, "Wow, you really made this easier for me"?
Here, there's nothing in the relative clause that points back to the head NP (a service). But in (3) there is something in the gapless relative that points back to the head NP (countless issues), namely the NP the issues. The issues is then anaphoric, but it's not a pronoun, so it shows properties of both the NoPro type and another type (called ResPrince in my earlier posting), in which a resumptive (anaphoric) pronoun is in alternation with a gap. And in fact
countless issues that ___ have scientific components but the issues are not seen as science issues
in (3) is very close to the ResPrince version
(4) countless issues that ___ have scientific components but they are not seen as science issues
which, in turn, is in alternation with the version with parallel gaps:
(5) countless issues that ___ have scientific components but ___ are not seen as science issues
I'm suggesting that we should recognize a hybrid "resumptive NP" (ResNP) gapless relative. Some of the NoPro examples in my earlier posting should probably be seen as instances of ResNP.
Note: the advantage of ResPrince relatives is that they mark the relativized element explicitly (thus lightening the burden on the hearer or reader), while ordinary gapped relatives have only implicit marking: in them, the position of the relativized element has to be determined by noting where something is missing within the relative clause. ResNP relatives, with lexical content (rather than just a pronoun) in the position of the relativized element, mark this element even more clearly (which is useful in (3), since the ResPrince version in (4) has a pronoun they that might at first be taken to be anaphoric to semantic components, rather than to countless issues).