They include prescribing the wrong dose, ordering medicines to be given at the wrong time of day, and giving patients two drugs with different names but the same function.
Junior doctors are most likely to make errors, according to the findings, with many blaming heavy workload, lack of time, and tiredness.
Charts belonging to more than 4700 patients, covering 44,000 prescribed medicines, were reviewed for the research, which involved staff from Glasgow, Edinburgh, Aberdeen and Dundee universities.
Errors were identified in more than one-third of the patient files examined and 7.5% of the prescriptions written contained an error. Mistake rates were higher in teaching hospitals, surgical wards and departments with a large patient turnover.
Professor Simon Maxwell, an expert in clinical pharmacology and prescribing at Edinburgh University, was involved in the study. He said: "There are an awful lot of things you can do wrong when you are writing a prescription. That is why it is probably one of the greatest challenges for doctors when they qualify from medical school."
He said whilst some of the errors were potentially serious, "almost none" had "significant consequences".
The Herald is running a campaign calling for a national review to consider the resources hospitals and care services need to cope with the ageing population.
Professor Maxwell said: "I would like to think we could do something to reduce the pressure on all staff. I think there is no doubt the through-put of activity has increased enormously ... We are treating an increasingly elderly and vulnerable population who are taking more medicines and who are more vulnerable to their side-effects and we have not seen staff increased to match that."
A working group led by the Royal College of Physicians of Edinburgh has created a chart for recording patient prescriptions in hospitals, which it hopes will be adopted across Scotland.