Hi JNChell,
I think it depends on many issues, but in general the cause for concern is a lack of consistency. BPD parenting tends to reverse the child-parent role so that children are expected to validate the BPD parent's emotional needs, instead of vice versa, with the parent validating the child's emotions.
In my experience, some kids can experience emotional enmeshment with the BPD parent, putting them at risk for all kinds of issues. So the child is put in a loyalty bind that deprives them the chance to develop a healthy sense of independence and self-determination.
There is a Lesson in the Coparenting section above about raising emotionally resilient children when one parent has BPD. The most important thing is to create a validating environment for your child -- this can feel counterintuitive if you grew up in a BPD home yourself, and requires some practice. Bill Eddy's book Don't Alienate the Kids is excellent, and so is I Don't Have to Make Everything All Better by the Lundstroms, which has a section on asking validating questions during different developmental stages. Essentially, you are helping your child recognize the emotional truth of their own reality (separate from mom's), and encouraging them to see themselves as capable and competent problem-solvers, instead of identifying with mom's victim-oriented thought patterns.
You may also want to read Richard Warshak's Divorce Poison so you know how to counter any parental alienation tactics. Dr. Craig Childress also suggests what he calls ju-jitsu parenting on his site, and refers to BPD parenting as "pathogenic parenting," an extension of the PD pathology that extends to the kids. His writing is what I find tediously academic but the information is priceless.
If you have a BPD parent, you may find that you have a much higher tolerance for emotional and psychological abuse, so it becomes a bit harder to see it in its full spectrum between your child and his BPD parent. I found therapy helped me be a much better parent -- I didn't even recognize what my ex was doing to our child as abuse and was a bit stunned to hear it described that way. That was 8 years ago. Now I see it clearly and feel tremendous sadness that I did not learn about validation until late in my son's life.
Your son is fortunate you are working so hard to change the family script. Listen to your instincts. They are good

LnL
Ju-jitsu Parenting: Fighting Back from the Down Position
C.A. Childress, Psy.D. (2013)