Please note that the check should work the other way round as well, i.e. disallow setting a mul label such that it, combined with the present item’s English description, conflicts with another item’s English label and description. Or another item’s mul label and English description. And of course the same for any other language as well. And this is where things may become tricky performance-wise (although I don’t know how this check is implemented, so I can’t tell for sure): if one changes the mul label of an item with n descriptions, the software needs to check 2n label–description pairs across all items in Wikidata, which is a huge increase from the current one item–description pair. I hope it will be possible to implement this without bringing down Wikidata (especially as one of the reasons for mul was to avoid bringing down Wikidata).

I agree a check should be implemented to avoid duplicates.