Big Paul made a series of mistakes, all of them potentially fatal:

--He was a recluse, holed up in his Staten Island mansion, never mingling with the troops or showing personal leadership;
--He involved himself in petty details that could have been handled by people way below him in the family;
--He made deals with other families that hurt his own people on the street;
--He carried on openly with his maid, Gloria Olarte, right under his roof, in front of his wife, a serious violation of Mob protocol;
--He failed to show up at Neil Dellacroce's funeral and wake, another serious violation of Mob protocol;
--The tapes that the government released after he was charged under RICO showed him disparaging the other Dons. They resented it, and also feared that he'd rat them out in order to buy a few more years with his beloved Gloria;
--Most important: he was greedy with his underlings, squeezing their earnings and earning their enmity. In Mobdom, always follow the money.

Gotti's murder of Castellano was equivalent to regicide and was not sanctioned by the Commission. But the reason Gotti got away with it is that no one within the Gambinos, and none of the other Dons except Chin, cared. Probably they were all glad Paul was gone.

Sure, he could have whacked Gotti first. But then another guy who resented him and Bilotti (maybe DiCicco) would have stepped in to finish him off.