Jamie Kightley lived in a one bedroom flat with his parents in Northampton
Experts have criticised a paediatrician who "apparently failed" to identify abuse injuries on a dead baby.
Jamie Kightley suffered brain injuries and more than 40 fractures and died at Northampton General in 2012.
Parents Jacqueline Parker, 21, and Adam Kightley, 24, of Northampton, are serving seven-year jail sentences for causing or allowing his death.
A serious case review found there were failures but, it concluded, they would not have prevented Jamie dying.
The report by the Northamptonshire Safeguarding Children Board - in which Jamie is given a the pseudonym Kieran - highlights concerns about the hospital and police handling of the case.
The author, Dr John Fox, said there had been a "significant breakdown" between police and the consultant paediatrician involved in the case.
The police, he said, arrived at the hospital one hour after their control room was informed of the death.
By the time police got there, the paediatrician who had failed to identify "significant child abuse injuries" had left to go to another ward, the report claimed.
Jacqueline Parker and Adam Kightley both claimed they did not harm Jamie
Dr Fox said: "It is my view that the failure of the responsible paediatrician to recognise the serious and extensive bruising on Kieran's [Jamie's] body as potentially being caused by child abuse is puzzling and very concerning."
According to the police, the consultant "declined" to speak with officers because he was "busy with another patient".
Instead, officers saw an accident and emergency doctor and Jamie's bruises were discovered.
Dr Fox added: "The paediatrician whose responsibility it was to co-ordinate and lead this multi-agency investigation into how and why Kieran [Jamie] died failed to do so in a reasonable and helpful way."
The report also identified that the primary professional working directly with the family after Jamie was born was a student health visitor.
Although Dr Fox said there was nothing to suggest the student's work had been at fault, he concluded the family was not one "suitable" for such an inexperienced health visitor to have been assigned to.
Six recommendations have been made by the review team including earlier systems for notifying police of child deaths and reassurances from the hospital about safeguarding training.
Assistant Chief Constable Russell Foster, of Northamptonshire Police, said: "We fully support the findings of the serious case review, in particular relating to the deployment of a detective inspector as lead investigator in cases of unexpected child deaths."
Northampton Hospital's Director of Nursing and Midwifery, Suzie Loader said: "We recognise that there are lessons to be learned from all agencies involved in this tragic case of physical abuse, and we have taken a very hard look at every contact we had with Jamie and his parents.
"We have already made changes to the way we work with families, both in pregnancy and when a child arrives at the hospital having suffered a serious physical injury."