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I agree and want to add the Gary Sinse(?) was broken too. Yet Forest stayed the course with him and turned his life around.
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Jenny was sexually abused by her dad.
Forrest shows up, and after having sex, she feels like she might have done the same thing to Forrest. In her mind, she sexually abused Forrest because he is not mentally capable of consenting. Do you see the parallel there?
That's the root of her internal conflict. She's terrified she's going to become her father and continue his cycle of abuse.
She eventually comes to realize that Forrest is more capable than she thought. However, she's a walking bomb of self-destruction at this point, and she knows it.
With the last ounce of selflessness she could muster, she leaves her child with Forrest. It was painful for her to lose the only two people who still love her, but any other action would ruin the child's life. At least, this is what she believes.
In the end, Jenny is a selfish and destructive person, but she abandoned love itself in order to save her child from her cycle of abuse. >

For the most part I agree with what you're saying, but what you're saying is the explanation for why she did the things she did, not justification for those things.
Someone can have really shitty reasons to do a good thing and really good reasons to do a shitty thing, but the end result is whatever actions were taken.  "Perception is reality" and "actions speak louder than words" basically, because ultimately we can't get in to other peoples heads for the exact reasons or motivations why they did something.  Sure we can guess, even take an educated guess if you know the person well and/or are a mental health professional, but no one except the person who's the subject, really knows the exact details of why someone does a particular thing.
The reasons explain the why, but they don't necessarily justify the actions.  Outside of her relationship with Forrest, Jenny continually makes really bad life choices and shows her self as someone who doesn't seem to place much value in others or herself.  So when you combine those actions with how she treats Forrest, while she may have reasons to do the things she does, the things she does are still ultimately pretty shitty. >

When a child is abused, it's much worse than an adult's excuse or a bad habit.
The abuse becomes normalized. Only strong minds are even able to recognize that their "normal" is wrong.
Most often, the child grows into an adult who doesn't know what a normal life should be nor how to achieve it. They have children, and the cycle continues.
Jenny continuously made bad choices. Yes. She never learned what choices were good.
It was never her excuse for bad choices. She tried making the right choices, but with a broken compass, she never had a chance. >

Sure, but again, saying she had a skewed life that set her on the wrong path is accurate and explains the why and sure, she becomes a more relatable and sympathetic character when you can understand the conditions of her life that helped set her on the wrong path.  You can even see a sort of valid logic to her decisions, given what her experiences in life have been.
But objectively speaking, if we’re judging someone, traumatic upbringing or not, her choices and actions are objectively shitty.  I think that’s partly what makes her such an unfortunate character.  You can see why she had some things working against her that would have skewed her life and feel a bit of sympathy for her,  like “this poor girl never had a chance”, but she so did what she did and has to own that.
Let’s us an extreme example to make a point.  Let’s say someone was brought up by a murderer, who didn’t hide from the family that they were a murderer.  The, the youth, sensed it was wrong, sensed it bad, but had no power to change or stop it.  So they grow, they move on from their parental unit because they know it’s a terrible place to be.
Whether through choice or through conditioning, or some combination of the two, they then take to assaulting others.  Mind you not killing, but assaulting.  On the one hand that person could be like “well at least I’m not my father” and you might even be able to understand that to someone brought up is such a traumatic fashion would normalize violence and so you can understand how they wouldn’t have the emotional development to refrain from some level of the violence they were raised in.  They may have been taught that it’s ok to kill someone who does you wrong, but this person is like “no, I won’t be like that”, so instead, in their skewed version of reality a beating isn’t that bad. 
You could understand why someone who got raised in a fucked up environment might think this way, doesn’t mean you agree, but you could understand that and you could reason it all out, again not justify it, but explain it all from a clinical sense.  But my point is that while you might be right that this persons trauma set them up for failure and that at least they aren’t the monster their dad was, objectively speaking, fucked up childhood or not, this persons behavior and perspective in reality is still messed up and dangerous.  You can sympathize with them for that even, but they’re objectively bad.
That’s an extreme example, but the point is that even through someone might not be the cause of their trauma, they’re still ultimately responsible for their choices and how they behave. >

Your comparison isn't fair.  Said simply, her dad harmed her, and this became her normal.
She knew that harming others was wrong, and she avoided harming others. In your comparison, the harm was "less" than the murderer, but he still intentionally harmed others. That's a key difference.
She tried living life doing the right thing, but the choices were always self-destructive because she didn't know what the right thing was. 
Her "normal" was self-destruction, which often hurt others close to her, but hurting others was never her intent.  She ran away from loved ones in order to "protect" them from her own self-destruction.
That's the key distinguishment.  Jenny intended to do good, but with a broken "normal," she often failed.
IMO, if she had stayed with Forrest, she would have likely ruined his life. >

So I agree with you in as much as she doesn’t ever display malice towards others in her life and so she’s never seemingly intentionally hurting anyone.
And I agree that her actions are mostly self destructive (though not entirely), or at the very least born out of self destruction.  That said, where I part with you is that, what makes her bad is that, self destruction is still ultimately destructive.  
We both agree that she’s a self destructive person and sure, there might be a sort of honor and empathy for others in recognizing your own self destructive tendencies and taking steps to avoid “collateral damage” to others, but when you get down to the core, self destructive is still destructive and try as you might, just as when a bomb goes off and you can’t make it only affect the thing you’re bombing, when a person is self destructive there is fallout that affects others.  
I’m not saying that intent doesn’t matter.  If you consider Jenny’s intent, she’s mostly trying to save others from herself and again, I can recognize a sort of honor in that and it does demonstrate she’s not a sociopath, she does have empathy for others.  My point is that, self destructive or not, she is ultimately destructive and thus she does shitty things, even she recognizes this about herself and seeks to save others from her shiftiness.
And again based on her upbringing and life overall you can see what led her down that path, you can understand the reasons behind that, and that makes her an sympathetic, unfortunate character in many ways, but at the end the day, abuse, self destruction, she still has to own her choices and the fallout of that self destruction. 
Good intent or not, her overall actions are still really shitty. >

But knowing all of this history, would you still call her a "monstrous POS" as in the OP? >

"Monstrous POS" no, again, I don't see malice on her part,  but a broken, destructive person, who lived a shitty life and made shitty choices that negatively affected others, yeah. >

I actually saw a video about that I cannot find anymore... the gist was that Jenny is actually quite the tragic character, because she is so defeated for most of the movie that her self-esteem is incredibly low, which in turn pushes her towards a bad crowd.
Forest, in her head, is someone that isn't supposed to exist - someone who loves her unconditionally. In her eyes, she is unlovable, so a large part of the movie is trying to bring out the worst in Forest because she beleives that he, like everyone else, will use and then drop her. Only at the very end does she realize that she had been a fool all along - at a point when it is much too late for her to make amends, so she at least tries to do the best for her son.
The overarching idea is that Jenny is broken and, to some extent, severely depressed, being unable to accept her own worth as a human worthy of love. 
Now, I don't know how well that is supported, but it is certainly a way to look at it. I also don't know if that would excuse her behaviour, but it would certainly explain it and put it in a very different perspective.