The report, by Healthcare Environment Inspectorate, found that progress had been made at the State Hospital at Carstairs, but inspectors discovered examples of stained bedding and cleaning methods that increased the risk of cross-contamination.
Staff did not know about the correct procedures for dealing with blood spillages and there were not always appropriate hand-drying facilities for workers.
Inspectors, who made an unannounced visit to the hospital in November, said: "Staff awareness of cleaning schedules and their roles and responsibilities for completing these to show that patient equipment had been cleaned was poor. Therefore, we are not assured that patient equipment was regularly cleaned or cleaned following each patient use."
They detailed four requirements for the hospital board to improve its standards within a month, saying it "must ensure that all patient equipment is clean and ready for use and be assured that methods are put into place to provide evidence of cleaning patient equipment following use".
Stephen Milloy, Nurse Director at the State Hospital, said: "We welcome the report, which highlights significant progress since the last inspection.
"We are pleased to note the inspectors' view that the standards of cleanliness in the hospital are very good, and the great majority of the relevant HAI standards are being met to protect patients, staff and visitors from the risk of acquiring an infection. We are committed to continuing to provide quality care in a safe, clean and comfortable environment, and have an action plan in place to address the small number of requirements."