Profile pictures—both the little one and the big banner one—are public. So, every time you change your cover photo or your profile pic, your past pictures stay public. The fact that you have changed your pictures stay public. And, the comments on those pictures are also public.
If that makes you squicky, you can do something about it ... sort of.
1. Hide your banner updates from your timeline.
If you don't want old banners (and their comments and likes) to remain public after you've changed them, hide them from your timeline by clicking the "Edit or Remove" little pencil icon and selecting "Hide from timeline." This will make all your old banners inaccessible from your public profile. You may also have to do this with your profile pictures.
2. Limit past posts
If you're a frequent photo-changer, you might want to try this option: Limit past posts. This will globally change all your previous posts to one privacy setting: friends only. It will also make your profile picture un-clickable, hiding those comments and likes from public.
This isn't reversable, so only do this if you're sure. I had a few old photo albums that I had made public or visible to"friends of friends," and this action affected those as well.
To do this, click on the little gear icon in the top right of the page and select "Privacy Settings." The option to limit past posts is the 3rd listed in the "Who can see my stuff?" section.
3. Watch what you say on other people's banners and profile pics.
Your comments or likes on other people's banners are public. If you don't want what you say on Facebook to be public, don't comment or like other people's banners or profile pictures. At the very least, be careful about what you say.
4. Check what people can see
All done? Check what people can see. Did you know that Facebook has a "View as" feature that lets you see what your profile and timeline look to the public or specific people? Access this through the gear in the top right, then click on "Timeline and Tagging" in the left-hand menu. The "View as" feature is the first in the "Who can see things on my Timeline?" section.
If you try these out and discover issues, corrections, or fun-filled facts, please let me know in the comments. Also, if someone has suggestions for hiding public groups and questions (the last remaining public things on my profile), please let me know.