They are both correct but have slightly different meanings.
"This mistake will prove to be of some value" suggests that you are trying to find something (anything) valuable from the mistake. You could exchange "some" with "little" and it would have the same meaning.
"This mistake will prove to be valuable" suggests greater value. I suggests that it might not actually be bad to have done this mistake now, and in the future under more important circumstances you will be pleased to have learnt from this.
Very high level usage - great!