We see when the twist is revealed that De Niro killed his wife by suffocating her with a pillow. But I'm pretty sure a post-mortem/autopsy is carried out on all suicide victims and that would've shown that she died of suffocation and that she didn't bleed to death. Therefore the whole film falls down from this point. Unless there's something I've missed, but I doubt it.
Yes the heart needs to beat to pump enough blood out of the wounds to result in death by slit wrists. Her body would have been full of blood.
sharequeman628 makes a good point here
http://www.imdb.com/title/tt0382077/board/nest/55239305?p=1
Florida, for instance, has a law to provide a mandatory autopsy for every apparent suicide victim, but in other states, it's up to the discretion of each county or medical examiner's office.
Autopsies cost on average ~$2000 each, the price fluctuating depending on how much testing needs to be done. It really comes down to money- if the county thinks there are no suspicious circumstances and they believe cause-of-death to be clearly suicide, they see it as a waste of the coroner's time (and taxpayer money) to perform a post-mortem.
So, just my long-winded way of saying it isn't necessarily a plot-hole that her body wasn't given closer examination.
what if he **** Spoiler***
only suffocated her until she passed out and then cut her wrist. Then no one would know