As an editor I catch a lot of things that other people, aside from other editors, wouldn’t. But if I edit two pieces of writing, one written by somebody else and one written by me, odds are that, everything being equal, the edited piece I wrote will have more errors. This seems counterintuitive but it actually makes sense upon reflection.
When you read somebody else’s writing with the intention of finding possible problems, you’re more likely to spot them than somebody who reads the same thing who isn’t on a similar search. But when you’re looking at your own writing, you think you paid attention to such things while you were writing it—and, subconsciously, you don’t expect to find anything wrong.
More, you know what you had meant to write. If a mistake was made, it’s most likely because your fingers mistyped something—not because you didn’t know what you were writing.
For example, I might type “Grimbsy,” a town outside of Toronto. I know what town I’m thinking about, and I expect that I will have got it correct. When I look at the word, I think to myself, “Yes, that’s right.” Except that it isn’t. The name of the town is actually “Grimsby.” (The correct version has “sby,” while the incorrect version has “bsy.”)
When you read your own writing you know what you’d meant to say. If your eyes see something wrong, you mentally translate it into what you expect it to be—and you don’t perceive the fact that it’s actually wrong. With somebody else’s writing, there isn’t this level of filter because you’re not as familiar with their thoughts and assumptions (and you don’t have the same “ego” that prevents you from thinking there could be something wrong).
This applies not only to spelling and grammar, but also to things like continuity, logical flow, and explanation. (Such as plot development and character motivation in fiction, and argument or thesis development in non-fiction.) If it’s your own writing, you may assume that something expressed makes perfect sense—but if looked at outside of your own understanding, the lack of an explicit explanation might make it unclear.
Add to this the fact nobody is able to spot every problem, and that the more eyes there are on on something the better, and it explains why everybody, even editors, should have their work double-checked.