Fine plaster dust inside AC vents

Turn the AC off before you start. Take the vent covers outside and wash them with a hose.

To clean inside the ducts, you must use a Shop-Vac with a HEPA filter and a fine-dust bag. A regular household vacuum will just blow the microscopic dust back into the room and burn out its motor. Vacuum as far into the ducts as you can reach, and change your main AC filter immediately.

If the dust went deep into the system, you may need a professional to clean the indoor AC coil. Drywall dust mixes with the coil's condensation and turns into a cement-like paste that blocks airflow.

For the tile grout, do not use water yet. If you mop drywall dust, it turns into a slurry and dries white all over again.

Vacuum the grout lines completely dry first using a brush attachment. Once the loose powder is gone, scrub the grout with warm water and a little white vinegar. The trick is to wipe up the dirty water immediately with a dry cloth. If you let it air-dry, the dissolved dust will just settle right back into the pores.