There is some black stuff which can be detached from the plant, what is this, some infestation/infection? thanks
Looks like scale insects to me.
I scrape them off with my fingernails but you can use a butter knife as well.
I've attached a link that should help.
Here is a link that might be useful: Scale on jasmines
i agree with Robert and if they are scale you can try rubbing alcohol works a treat get a small brush dip it in the rubbing alcohol and paint it over the scale will kill them fast and you can tell when they are dead as they brush of easy