I recently decided to remove some information from my profile so rather than make the same edit 42 times I decided to use the relatively new option of only copying the changes rather than copying everything. So I edited my Stack Overflow profile and then clicked the "Save and copy changes to all Stack Exchange communities" button.
I did this on Thursday 23rd October, and didn't notice anything untoward. I wasn't online on Friday, but when I logged in this morning (Saturday 25th) I discovered that all my profile pictures had been changed to by Stack Overflow one. Where I can check* I can see that I have a "user switched profile image to imgur" entry at the time I made the change on Stack Overflow.
However, according to the information I can see on my Stack Overflow profile it also claims I changed my profile image on Thursday when I know I didn't. It seems that changing any other data on the profile also updates the image.
NOTE: When I copied the the other profile changes it only showed those changes I expected in the confirmation dialog.
* one of the perks of being a mod.