The stone like socle in the shrine.
What does 問題の add? My take would be something like "The shrine in question"
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The 問題 is used in the following sense.
I think in question is fine. Another alternative is under discussion.
edit: I actually didn't realize
問題 had the meaning mentioned in sundowner's answer. That seems more likely, although certainty would require more context.
の for connecting nouns is really flexible, and can mean quite a few different things based on context. In this case, it's talking about the
shrine which is the problem. You could also write this as something like
問題になっている神社; the most natural english translation I can think of is
the problem shrine.
Incidentally, I'm not sure if the quote in your answer was intended to be a translation, but
問題の神社にも岩座があったっていうし is something like
They say there was a stone socle in the problem shrine as well.