Is this sentence right?
Is not there any problem can aim for and is not to ...
Perhaps the best politicians can aim for is not to make things worse for friendship.
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This is perfectly fine, though confusing. You are possibly missing some of the grammatical structure, as it has an embedded clause with the complementiser "that" omitted.
It is exactly equivalent to:
Perhaps the best that politicians can aim for is not to make things worse for friendship.
where "that politicians can aim for" is a relative clause qualifying "the best".
I would call this a Garden path sentence, as it is only when you get to "is" that you realise that the natural construction up to that point must be wrong.