Is breakthrough bleeding between periods reason for concern? or usually not a big deal?

Not usually: Break through bleeding (btb) while on hormonal contraception is very common and not serious - only a nuisance. Btb on natural cycles is usually due to hormonal changes at ovulation, and again it is not serious. There are also less common causes (polyps, fibroids, cervical ectopy, cervical cancer) and your gynecologist can help you determine if you have any of these.