A sample size of one is more than enough for internal validity, assuming I take enough data points to detect an effect. (I typically do 20+ pairs; the stronger the effect, the less you need.)

What n=1 threatens is any kind of external validity, that is, whether one would observe the effect or lack of effect in someone other than me. I may find that potassium is fantastic for me, but that tells me very little about whether potassium would help you or anyone else on this page.