what's the significance of...(little spoiler)

It ultimately gives a clue of the type of person he is.

Regardless of whether he killed his wife or not, he clearly can't have been too fussed if he was sleeping with someone else just a few days later.

yeah, pretty much what everyone else has said. In the book there is one point where he tries to claim that he killed his family because they were in such a bad situation financially that they were homeless and living in a campsite or a few months and he had racked up a ton of credit card debt and stolen a minivan and he says he killed his family so they wouldn't have to suffer any more but it was more like he wanted to kill his family because they were dead weight and he wanted to be able to just start over with a stolen identity (not only was he using Finkel's name but had stolen someone's credit card number from the startbucks he worked at and bought a deceased peron's social security number online)

deleted scene?

It shows his lack of remorse immediately after.