Are you manually creative the bullets or are you using the bullets and
I am using the Bullets and Numbers feature.
The bullet from Bullets & Numbers takes its style from the text next to it, unless specified otherwise (by specifying a character style in the B&N dialog).
What appears as a checkbox on your screen is just a lowercase 'q' (only its image is 'wrong'). When you apply Caps, All Caps, or Small Caps, it is replaced with the image that's behind the uppercase 'Q' -- an airplane.
I don't get the same thing; my version of Wingdings must be newer than yours. Modern fonts are re-coded in a slightly different way.
You can try to fix it this way: create a new character style and set the text Case to "Normal", then apply this character style to your bullets. Disclaimer: I don't get this weird behavior so I cannot try myself.
That did it! Thank you! I had tried to set a separate Character Style for the bullet before, but did not set 'Case' to 'Normal'. That was the fixer.