Had ovarian cyst but it shrunk. I'm still taking birth control pills daily. I've been spotting/mild bleeding some days, doctor says it's normal. Is it?

Not uncommon. Some women have spotting or light bleeding while using a birth control pill. This is unlikely to be anything dangerous but can be quite annoying. This will often stop after a while on its own. If the problem persists you could take a low dose estrogen for a few weeks, change pills or change your method of contraception. Hope this helps.