The survey, covering five years of work at a paediatric teaching hospital in Scotland, revealed fewer mistakes than expected.
But the level of secrecy surrounding the blunders did surprise the researchers.
It found that one mistake occurred for every 662 patients admitted to the hospital, although most of these happened in children under the age of two.
Three-fifths of the mistakes happened on medical wards, and six out of ten were made by nurses, rather than doctors, as nurses are often responsible for measuring out the right quantity of drugs for patients.
Most errors minor
Most of the errors were classed as "minor", even though 10% required some extra treatment to rectify.
The study authors said they believed doctors and nurses in some cases recorded the incident as minor in order to deflect criticism and possible repercussions.
James Paton said: "Some errors were minor, some were pharmaceutical errors, nurses saw the errors being made and the mistakes were corrected before the drugs were administered.
"The important thing is that these are errors in the system and if we stop the minor ones now then we will stop the bigger ones in the future.
"Most were related to drugs, giving wrong dose, giving incorrect drugs etc. I think we can give reassurances, but I think parents should be informed about the errors.
"About 60% of errors were related to doctors and nurses and I think it merely that figure reflects that drugs are administered by human beings. About 4% could be considered serious, but there was no adverse effect on the children and they all recovered."
Extra checks
In 15 cases, the error involved giving either 10 times too much, or 10 ten times too little of the drug concerned - an error which can prove fatal in some circumstances.
Many of the mistakes involved anti-cancer drugs, intravenous feeding or fluids.
Encouragingly, however, the research found that when extra checks and training were put in place by the hospital, the error rate dropped significantly.
Mike Stone, of the Patients' Association, told BBC News Online: "It's not in the spirit of openness if doctors are acting as Gods and withholding information that patients need.
"There should be complete openness, that's very important after Alder Hey, Bristol and North Staffordshire.
"Fortunately there are younger doctors who have had some communication training, but when something like this happens, it shows that there is still an awfully long way to go."
The research was published in the journal Archives of Disease in Childhood.