Daniel McSwiggan, 69, who had Alzheimer's disease, was last seen in Motherwell, North Lanarkshire on September 12.
His body was found at Strathclyde Park golf course on September 26.
Concerns about the handling of the search were raised by the Mr McSwiggan's family and the case was referred to the Police Investigations and Review Commissioner (PIRC).
Investigators interviewed family members and medical professionals, as well as examining statements from officers and police command and control room records.
PIRC concluded that the case should have been treated as high risk, rather than medium risk.
"It should have been evident to Police Scotland that the man was a high risk, vulnerable missing person and Police Scotland should have graded the missing person assessment as high rather than medium risk," the report said.
"Although the investigation found that Police Scotland's initial actions were appropriate, it also found that it could have managed some aspects of the enquiry better."
PIRC also found that some officers did not keep notes of decisions made during the investigation, written statements were not taken from a number of key witnesses and CCTV footage, although viewed, was not seized and was lost.
One of the last sightings of Mr McSwiggan was on a bus but some officers working on the search were not aware that they could access travel information from the bus company, PIRC said.
The commissioner, Professor John McNeill, has recommended that a dedicated team for the management and conduct of vulnerable missing person investigations is set up.
Prof McNeill said: "There are lessons to be learned from this case. In particular, appointing a senior investigating officer, a dedicated person for family contact and a dedicated enquiry team at the earliest stage of the enquiry, may have alleviated family contact difficulties and reduced the family's distress.
"My investigation found that a number of officers were not aware of the memorandum of understanding between the bus company involved and Police Scotland that allowed information on travel concession cards to be used as a way to trace the movement of individuals.
"In my view, this lack of knowledge significantly hindered progress of the investigation and should be addressed by an awareness-raising exercise within Police Scotland.
"I have also asked Police Scotland to stress to staff the importance of obtaining written statements from significant witnesses and emphasise the importance of early seizure of CCTV footage."