If you're using a font that doesn't actually have an italic variant installed, trying to make some instances of that font italic can cause issues when printing. You may want to look in the system font settings (Start → Settings → Personalization → Fonts) to see if the font you're trying to use has an italic face.
The issue is that the ceiling finish in the family room and the hallway is different from the ceiling finish in the dining room and kitchen, as you can see if you delete the tray ceiling:
Tray ceilings will "flood fill" into adjacent rooms through invisible walls if the ceiling heights are the same. This is useful for non-recessed tray ceilings, but it's admittedly less useful for recessed ones. Changing the ceiling material in those rooms to all be the same color would fix the warning. Alternatively, if you want to keep the color difference, you can use the "Explode Tray Ceiling" command to break the tray ceiling polyline down into its component ceiling planes and then pull back the large "outer" ceiling plane that has overflowed into the adjacent rooms:
BenMerritt's post in Layout Export to PDF Sends wrong fonts was marked as the answer