Daniel Sanzone was jailed for life after shaking two-week-old Joshua Millinson in Wolverhampton in 2015.
However, there was no evidence injuries that caused his death could have been anticipated, a safeguarding board said.
But it said staff were not questioning enough of the "concerning history" given by his parents.
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The review looked at two visits to New Cross Hospital's emergency unit by Joshua with Sanzone and the baby's mother, Zoe Howell, before the fatal shaking incident at their home in Pendeford.
Sanzone's trial had heard a nurse and a junior doctor assessed Joshua and found no swelling and no pain but later bone experts suggested he had suffered some leg fractures at this point.
However, the review found the fracture would have been very hard to identify in a baby so small and no X-ray was taken.
But the report said the conclusion that there were no safeguarding concerns was "reached too quickly" on a second emergency department visit.
It added although the evidence was "it was carried out competently, too much reliance was placed on the medical examination" of Joshua, which proved normal, and "insufficient account was taken of the concerning and inconsistent history given by his parents".
The review, commissioned by the Wolverhampton Safeguarding Children Board, made a total of 12 recommendations on how various public bodies could improve their practices.
It said the Royal Wolverhampton NHS Trust should review safeguarding arrangements in the New Cross Hospital emergency department and in antenatal services.
Wolverhampton City Council should also audit the effectiveness of local authority child and family assessment, the report said.
It added the National Probation Service in the Midlands should ensure risk assessments "are updated when there is a change in the circumstances of a supervised offender which may indicate a heightened possible risk to vulnerable children or adults".
Board chair Alan Coe said the report identified "a number of ways in which, in similar circumstances, more opportunities might be taken that could enable professionals to better coordinate and share information and to identify potential risks".
He said: "Actions are being taken, including the Royal Wolverhampton NHS Trust implementing new guidance for Emergency Duty staff about children who present with unexplained or inconsistently explained injuries, reviewing procedures in maternity services and updating training accordingly.
"[They also include] the council ensuring social care professionals clearly understand their responsibilities around pre-birth assessments and referrals and the National Probation Service ensuring that assessments are updated when there is a change of circumstances involving a supervised offender which may indicate a risk to others."
In November, Sanzone, 23, was convicted of murder and sentenced to a minimum of 15 years in prison.
Ms Howell was cleared of child cruelty and causing or allowing Joshua's death.

The man was walking near Slieve Binnian on Monday when he fell at about 16:30 BST. Other walkers spotted him and raised the alarm.
A team of 18 people from the Mourne Mountain Rescue Service helped the man before he was airlifted to hospital.
The man had been in a place known as the water slabs, said Martin McMullan, a rescue team coordinator.
He described the area as very slippery and quite challenging.
"It seems that he lost his footing at the top and then slid down part of the water slabs and started to tumble before he came to rest at the bottom," said Mr McMullan.
"He had taken quite a fall and sustained multiple injuries primarily to the upper part of his body.
"We treated him for head, neck and chest injuries as a result of that fall."
The Mourne Mountain Rescue Service was also involved at the weekend in the search for the two missing crewmen of an Irish Coast Guard helicopter that crashed off Blacksod in County Mayo.
Both men have been missing since Rescue 116 crashed on 14 March.
Hospital staff were too quick to assume there were no safeguarding concerns in the case of a baby who died after being shaken by his father, a report says.
[NEXT_CONCEPT]
A man is in a critical condition in hospital after falling up to 50 metres in the Mourne Mountains.