Am I crazy?

Yup, looks definitely like a hot pixel, or actually a "stuck" pixel, as it happens even at faster shutter speeds. Just from my quick google search, it doesn't look too good right now. Looks like I'll be making friends with Canon's service dept.....

I can see the focus points in BreezeBrowser Pro, but there is no indication which point is the active one.

In all three images, none of the points are right on the subject's eyes. In the image of the young lady, the point closest to her face is on the hair just to the left of her chin, in the image of the youg man in the brown shirt, the closest focus point is on his cheek to the left of his nose and in the image with the airplane in it, the closest point is on his hairline above his right eye.

You can attempt to fix the hot pixel yourself. Put the lens cap on. Go to the menus and select manual sensor clean. After 30 seconds turn off camera to reset the mirror and shutter. Turn the camera back on and take a test shot.

Several people have had good luck with this method. You can search for "hot pixel" to see the posts.