Inspectors also noted "poor compliance" with standard infection control precautions in the unit at Dumfries and Galloway Royal Infirmary.
The Healthcare Environment Inspectorate (HEI) has issued eight requirements and three recommendations for NHS Dumfries and Galloway to address.
Inspectors found that the standard of environmental cleaning in the intensive care unit (ICU) was poor and some patient equipment was not clean when they visited the hospital on January 15 and 16 this year.
They noted dusty equipment including ventilators, drip stands and blood pressure monitors, and dust in patient bed areas, a treatment room and storage areas.
The inspectors also found poor compliance with standard infection control precautions in ICU, where they noted nursing and medical staff moving from patient bedsides to other areas of the ward without removing their protective equipment.
HEI chief inspector Susan Brimelow said: "We have identified a significant number of high priority areas where Dumfries & Galloway Royal Infirmary must make improvements within one month.
"During inspection on January 15 and 16, we were not satisfied with infection prevention and control practices seen in the intensive care unit.
"In particular, we found the standard of cleaning was poor and patient equipment which was not clean. We escalated our concerns on the day of inspection and revisited the hospital on January 22 to follow these up.
"After revisiting the ICU, overall, we feel assured by the steps being taken by NHS Dumfries & Galloway to resolve these issues."
The inspectors also noted inappropriate storage of equipment in ICU, including open boxes of sterile stock items on the floor of the store room, in the main corridor area and on the worktop of the unit's treatment room.
They also found that cleaning schedules did not accurately reflect the activity or equipment found on the wards and units inspected.
However, they found that in most areas inspected the standard of cleaning was good, staff demonstrated awareness of infection prevention and control policies and procedures, and patients with a known or suspected infection were being cared for appropriately in isolation.
The inspectors issued eight high priority requirements which must be addressed within a month.
These include ensuring that all staff are aware of the procedure for the management of blood spillages and the cleaning of contaminated patient equipment, and that the ICU is cleaned in line with the requirements of NHS Scotland National Cleaning Services specification.
The health board has also been asked to ensure compliance with the use of colour-coded aprons in ICU to reduce the risk of infection and that all hand hygiene products are suitable and fit for purpose.
Inspectors said they will follow up these concerns at future visits.
Jeff Ace, chief executive of NHS Dumfries and Galloway, said: "The report does not identify harm to patients and the board has great confidence in the staff and in the standard of care provided in our ICU.
"The report does, however, identify environmental and other latent risks, and we have moved extremely quickly to address these.
"I would like to express my thanks to all of the team who have worked very hard to address the HEI recommendations in such a short space of time."
NHS Dumfries and Galloway said that it responded as a matter of priority to the HEI recommendations, most of which have already been addressed or are at an advanced stage of implementation.
It said that the HEI concerns that relate to the standard of cleaning and the storage of equipment are in part associated with the physical limitations imposed by an ageing ICU and that the new hospital which is to be built will eliminate many of these problems.