Inspectors found blood contamination on items including a glucometer and faecal contamination on toileting equipment such as commodes and raised toilet seats at Ninewells Hospital in Dundee.
They also found "significant levels" of dust on high level ledges in the special care baby unit of the neonatal department, and on two patient bed frames in the intensive care unit.
Healthcare Environment Inspectorate (HEI) has detailed nine requirements which NHS Tayside must address as a matter of priority in its report on the unannounced inspection, carried out on March 11-12 this year.
The requirements covered a range of areas, from cleanliness to staff dress code and breast milk storage.
Inspectors found there was "poor compliance" with procedures for managing sharps.
Four sharps bins, including one in the neonatal unit and another in the acute medical unit, were found to be externally contaminated with blood, while two elsewhere were overfilled.
HEI said NHS Tayside must address the problem to "reduce the risk of needle stick injury and infection to patients, staff and visitors".
Inspectors found the standard of cleaning varied across the wards and departments they visited.
The frequency of cleaning of the neonatal intensive care unit did not meet national requirements, which the health board has been told to address.
Susan Brimelow, HEI chief inspector, said: "This inspection has identified several priority areas where NHS Tayside must make improvements within one month. These include staff adherence with dress code policies, the cleaning of patient equipment, breast milk storage arrangements and the cleaning frequency of the neonatal unit.
"However, staff demonstrated a good understanding of the process to follow when a patient with known or suspected infection was on their ward and patients commented positively on the standard of cleanliness on their wards.
"This inspection resulted in nine requirements which NHS Tayside must address as a matter of priority. We will follow up these concerns at future inspections."
The inspection team also noted that not all staff were complying with the NHS Scotland dress code policy.
Six staff were seen wearing theatre clothing, including theatre footwear, in the main concourse area of the hospital.
Two doctors with long sleeves were seen in the acute medical unit, while one doctor there had untied hair.
HEI found that overall, NHS Tayside is complying with the majority of NHS standards to protect patients, staff and visitors from acquiring an infection.
All patients with a known or suspected infection were isolated appropriately while all staff groups were clear about their role when prescribing antibiotics to hospital patients.
NHS Tayside has produced an action plan detailing how it is addressing the nine requirements.