Stupidity: Ashley Judd finally tracks her husband down and what does she do? She doesn't try to capture him to prove her innocence, she doesn't notify the police, she doesn't take his picture and send it to every police dept in the US, she doesn't even follow him to find out where her son is. Instead all she does is ask for her kid back. What was she going to do even if she got him back? She is still on the run from the law, with little money and resources and she doesn't even know if her kid even remembers her.
Factual error: Ashley Judd is convicted of murdering her husband for the insurance money and that would make it a first degree murder charge (first degree meaning she planned the murder). Because of that there is no way she would have been eligible for parole after just 6 or 7 years.
Suggested correction: It's never stated that she was charged with 1st degree murder, nor that she killed her husband for the insurance money. It was only brought up in trial as motive. Nick's accident was ruled "wrongful death" and the fact she did get paroled further show she was never convicted of 1st degree murder.
And what about the phone call from prison the Libby makes to Angie, and Angie says she "was just about to call her" or she tried calling her like how the heck can you call someone in prison!?
Plot hole: For a convicted murderer who violated her parole and assaulted her parole officer while escaping custody, Ashley Judd moves around the country and even boards airplanes with little to no problems.
Suggested correction: She was simply careful. There's constant manhunts for much more serious felons and parolees on the lam who seem capable of moving around without getting caught.
Other mistake: When Nick is confronted with the evidence against him at the end, Tommy Lee Jones says they found a shovel and dirt in Nick's car trunk. But Nick didn't bury her, he locked her in a concrete tomb.
Suggested correction: They were saying this was how they were gonna frame him, not what he actually just did to her.
Suggested correction: As you said, she's on the run from the law. Why would she call the cops and risk going back to prison and losing her son again? Even if her husband was alive, she has no way of knowing what will happen to her. This was her best shot (especially in her mind) to getting her son back, thinking her husband would rather give up the boy's location rather than die; whereas height keep the boy's location a secret if all he was facing was possible jail time, if that.