Some things to point out:

It wasn't so much that Paul had a woman on the side, it was that he did it in the same home as his wife that was considered extremely disrespectful.

Paul also sided with Chin and the Genoveses over his own family on certain construction matters which was viewed with disdain.

As far as wakes are concerned... the Anastasia situation and the Dellacroce situation are two entirely different animals. Anastasia was killed from within, Dellacroce died by natural causes.

The difference between meeting at Paul or Carlo's house and meeting at the social club was that the former were private residences and the latter was a public place, and one known to be under constant surveillance at that.

The reasons Paul was killed have traditionally been given for the following reasons:

1. He was seen by many as more of a businessman instead of a gangster. He didn't earn his way into family any more than he had to earn his relationship with Gambino. He was viewed as undeserving of the title of "boss" while someone like Neil, who had infinitely more knowledge of the streets, was seen as disrespected. This may not have been enough to kill Paul alone, but...

2. Gotti's crew dealing drugs and the Ruggiero tapes became a major source of contention as John feared that their revelation would bring about the demise of himself and Ruggiero. Once Neil died, he lost his buffer and feared that Paul would either kill or demote him, with obviously neither of them being an acceptable option. Additionally, Paul was suggesting a leadership change which was unacceptable to John in addition to the other co-conspirators. He was also seen as someone who could potentially be turned, as his posh lifestyle had softened him enough that he might not be able to stand a significant jail sentence. Not attending Neil's wake was the final, unnecessary nail in Paul's coffin.