I'm having trouble with seltenen. What does it modify? Not »einer« (singular nominative), not »jener Fälle« (plural genitive), it could be dative plural »denen« but it doesn't make sense to agree with the object of the relative clause within the main clause. (Or does it?)
Das Ergebnis war purer Zufall gewesen oder einer jener – in der Wissenschaft gar nicht so seltenen – Fälle, in denen man erkennt, was man erkennen will.
It is genitive plural:
jener seltenen Fälle
plus the information of where the cases are gar nicht so selten (in der Wissenschaft).
It is important to realise that the entire fragment that is troubling you is an apposition of jener Fälle. This could also have been phrased e.g. using a relative clause as follows, but the author decided against it.
Das Ergebnis war purer Zufall gewesen oder einer jener Fälle, die in der Wissenschaft gar nicht so selten sind und in denen man erkennt, was man erkennen will.
Thus, seltenen is a direct modifier of Fälle which is in genitive plural. The key here is that you can imagine the entire phrase as being one attributive modifier and because there is an article you would use weak declension. Compare below:
Das Ergebnis war purer Zufall gewesen oder einer jener in der Wissenschaft gar nicht so seltenen Fälle, in denen man erkennt, was man erkennen will.
