См. также: по подозрению, по подстрекательству, по традиции, по форме или преимущественно по форме
You can say that something is done in error. This is a fairly formal use. They had arrested him in error. (Collins COBUILD English Usage)
In conversation, you usually say that something is done by mistake. I opened the door into the library by mistake. (Collins COBUILD English Usage)
