My favourite writer error is forgetting that every character has their own motives, and most of them are unrelated to the protagonist. The most amazing thing ever is when a rival, nemesis, or casual bystander is to all appearances completely obsessed with the protagonist to the point that they appear to have shaped their lives around the protagonist. The protagonist is all they talk about. Thoughts of the protagonist keep them up at night. They constantly compare other people to the protagonist. They mock the protagonist, because they can’t seem to stop thinking, staring, or obstructing the protagonist in some way. You know it’s unintentional, but all else being equal, this character appears to have a raging crush on the protagonist, one that only true love’s first kiss can subdue.
I call it the Draco Malfoy Syndrome.
And see, this is the real problem with Mary Sues. Not their excessive perfection, but the way they distort the story’s center of gravity, so that everyone’s lives revolve around them. Everything is about them.