Does Using Retin-A Reduce the Effectiveness of Birth Control Pills?

There is no interaction beteween birth control pills and Retin A.  If the birth control isn't helping your acne, I would see your dermatologist as there are many other treatment options available.

I think you are confusing the issue of birth control pills and oral antibiotics.
There would be no theoretical risk that a topical Vitamin A product would have any effect on oral administered birth control pills.
As far as birth control pills and oral antibiotics, we have a situation in which their is a theoretical risk. Some people, mostly trial lawyers, maintain that antibiotics can displace the estrogen from its carrier protein thereby lessening the potency of "the pill". Secondly, by decreasing the transit time of ingested material, less oral contraceptive is absorbed. Also, by killing the normal flora in the gut there is less of what we call the intrahepatic circulation ( this is the means in which the bacteria break some molecules down which are delivered to the liver and recirculated).
None of this has been proven out in the literature. Both dermatologists and gynecologists are in general agreement that antibiotics do not inactivate birth control pills. However, since package inserts state that there MAY be an interaction, a prudent physician, fearing the wrath of the legal profession, will dutifully warn patients about this potential interaction.
No such warning is needed in regards to Retin A