[OuTcAsT]

Sorry, I was referring to a later news posting than the one presented in this thread that said that the wife had a seizure which caused her black-out and the birth - no mention that she had any history of seizures. Could this have been anticipated? You decide.

The article in the OP is very clear about the fact that the wife was experiencing an amount of pain the evening prior, that was alarming enough for her to consult a doctor, and make an appointment. While it is impossible to say for sure, the pain, (in her lower back) might indicate a premature onset of labor. The premature labor may have been the proximate cause of the seizure, rather than the opposite. Not stating fact, just speculation based on the story.

I don't think we have enough information to place al blame on the wife or husband.

On this point, I disagree. They both knew that there was something not quite right or, there would have not been enough concern to warrant a Doctors appointment.

I don't feel it unreasonable to think that they should have sought immediate medical attention, or at the least, the husband should have kept her under observation until the appointment, either directly, or through friends or family.

Regarding other investigation options -

How about contacting the landlord (who has the legal authority to enter the apartment) to come and inspect the apartment. Not illegal and no lawsuit,

First off, you are incorrect on a couple of the finer points about landlord rights, The landlord can inspect the property, but this usually requires advance notice, and, permission. Usually a landlord can only enter the apartment with that permission, or on an emergency (Fire, Flood) basis. Otherwise, it is illegal.

Now, Had the Husband called the landlord, and requested that he enter, that could likely have been done. The police, however, do not have the authority to make such a request. it would be the same as kicking the door.

If LEs only look for evidence of a crime, why weren't emt's called or also called to the site?

While I will not speak for LE, in general, a welfare check likely would include looking in windows, knocking on and checking doors, listening for moans, yells, screams, or any signs of trouble.
As an EMT, I can tell you that there is no evidence that I could find, that a cop would not also recognize as a sign of trouble. (Incidentally, lots of, if not most, LEO's are cross trained as medical first responders, EMTs or Paramedics.

Sorry to tell you, but this was not a failure of LE, to do their job. It is a failure of people taking personal responsibility for their own well being.