Final answer:
The owner's agent should disclose the issue of water stains to the buyer and suggest a professional inspection to determine the extent of any water damage.
Step-by-step explanation:
When an owner's agent is showing a buyer an apartment building and the buyer notices water stains on the ceiling, the agent's best course of action is to disclose the issue promptly to the buyer and recommend a thorough inspection of the property to assess any potential water damage or related problems. It is important for the agent to act professionally and to maintain ethical standards by not concealing any defects they are aware of, as this could lead to serious legal and professional repercussions.