General questions
Do they clean the entire cooling and heating system, including ductwork, equipment and all of there parts?Basically, everything that the air moves across, is it cleaned?
What do they know about A/C systems? Are they air conditioning contractors, janitors, carpet and drapery cleaners? If they do everything that should be done, they will be inside your ducts and equipment. Would you let the guy at the car wash work on your engine?
Do they use non-toxic cleaners? This stuff will be in your duct system and you will be breathing it.
Do they have the proper system cleaning equipment? Low pressure and low volume vacuums don't remove the debris effectively.
Is the vacuum exhausted outside the building?
Do they have suitable positive air pressure (160-200psi)?
Does their equipment completely clean twists and turns in the complete duct system?

Plenums and Chases
Plenums and chases are not be used in all systems. A plenum is typically an enclosure that various small ducts attach. It could be a built-in box that a furnace would be mounted on. In this case, the return air grill could be mounted to the plenum. Noisy, but it's cost effective. With multiple return airs in the building, there would be ducts coming to the plenum. This same principal is also applied to the supply air side of the system. Although, this is not an efficient (air flow) design practice. A chase is a hidden cavity that is used to connect ductwork in the walls. As an example, it could run floor to ceiling, connecting a crawl space to an attic. In both of these designs there is a possible problem. Quite often, NO ductwork is run through these spaces, they allow the space to be the duct. Drywall, 2x 4's, maybe even building insulation are now in the air stream. These spaces not only need to be cleaned ,but they also need to be completely inspected for air leakage, mold, water intrusion and insulation. This is an area that is known to accumulate large amounts of debris due to the interrupted air flow.

Metal Ducts
Are all interior ductwork surfaces free of debris? Another item to look for is residue from cleaning solutions.

Fiberglass Ducts (Duct Board)
This material is not cleanable without eroding the surface. The surface layer is covered with an encapsulant to keep the fibers in place. This layer will degrade over time. Friction from cleaning will aggravate this condition. Fiber will then escape into the air stream ready for you to breath.

Flex Ducts
Generally this is cleanable ductwork. However, care must be taken to ensure that the lining is not damaged. Most flex duct has a thin, cellophane like liner. Do they know how to do this without damage?

Equipment
If it is on a plenum, will they clean the plenum? If it is in the attic or a crawl space, will they go in and clean it? If it's a gas furnace, do they clean the heat exchanger?
If it's an electric heater, do they clean the heat strips?
If it's a heat pump or has cooling, do they clean BOTH sides of the evaporator coil (the part that makes the air cold)?
If it has a evaporator coil, do they check for and eradicate mold growth without spreading it further into the system?
If it has a evaporator coil, do they clean the coil cabinet?
If it has a evaporator coil, do they clean the condensate pan and check for proper drainage?
If it has a evaporator coil, are they properly trained AND licensed to handle CFC's (refrigerant). Some coils can only be cleaned after removal. This means the refrigerant lines need to be cut. The refrigerant needs to be removed and stored. After the cleaning process and line repair, it can then be put back in the unit.
Do they clean the blower?
Do they clean the blower motor?
Do they clean the blower cabinet?
Will they remove the blower if necessary to clean it properly?

Diffusers, Registers and Grills
Do they remove all diffusers, registers and grills, clean them and then reinstall them level and secure?
Do they know what a diffuser is?

Filtration
Do they replace the filter? Not a spun fiber filter, they're junk. Also be weary of electrostatic filters. Some of the claims are questionable. Did they offer any suggestions on filtration. You just paid real money to have the system cleaned. Improvements in filtration could keep them from coming back for a long time. Poor filtration is the number one reason for dirty ductwork and indoor air quality (IAQ) problems.

When they are done

Access Panels, Doors and Covers
Are reinstalled access doors attached with more than just duct tape (screws, rivets, etc.)? Foil tape does seem to hold up well.
Do any of these items leak air?
Did they need to cut in any new accesses? Where these sealed correctly?

System Operation
Cycle the system using the thermostat.
Does the blower work in "Manual"?
Set the blower to "Automatic".
Does the heating function?
If it has cooling, does it function?
Are there any new sounds? There have been occasions where the blower was very dirty. After cleaning, the air flow was returned to the designed condition, resulting in increased air flow and more flow noise.
Where the diffusers, registers and grills reset for proper air volume and flow pattern?
Did they clean up after themselves?
Did they leave an oil stain in the driveway?