Simple registration form with Backbone
Generally it looks like your know what your doing, maybe you could be more efficient by removing the blur event since you wouldn't need to save/validate if the input is already populated or left empty, this will also save you calling onInputChange twice when an input is changed.

Backbone will automatically create this.$el from the el property so you can just do.

el: 'form' and then this.$el would be created for you.

Finally i would use listenTo rather than on for example.

this.model.on('invalid', this.onModelInvalid, this);

would be done like this using listenTo.

this.listenTo(this.model, 'invalid', this.onModelInvalid);

This allows you to keep track of events on the object and then remove them all at once later on.