The big negative things from Karen's 616 history that I think are most likely to come up are her stint as a heroin addict who worked in pornography to buy drugs (which in the comics happened significantly after she met Matt and Foggy) and her father's, uh... let's go with 'legal woes and mental breakdown'. (Long story short, Dr. Page was a scientist who invented a new superweapon, refused to sell it or reveal its secrets to the US government, was tried for treason as a result (which I am pretty sure is not how treason even works), went crazy from radioactive side-effects of his own research, also got superpowers via radioactive side-effects, faked his own death, rode a skeletal horse (because by that point, why the hell not), and tried to kill Matt and Karen before briefly coming back to his senses and saving them at the cost of his own life. Silver Age comics were weird.)
I tend to go with some kind of drug problem, possibly with some related criminal activity given that Karen heavily implies she's shot at least one person before she kills Wesley. Family issues could certainly play into that, though -- the MCU military is not above highly unethical conduct, as seen in the Hulk movies, and the stress of unfair accusations against her father (not to mention him possibly going crazy and/or vanishing) could have been one thing leading her to try drugs as a coping method, and would also be fairly easy for Ben Urich to dig up and point out as a factor reducing Karen's public credibility as a source in the Union Allied investigation.
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The big negative things from Karen's 616 history that I think are most likely to come up are her stint as a heroin addict who worked in pornography to buy drugs (which in the comics happened significantly after she met Matt and Foggy) and her father's, uh... let's go with 'legal woes and mental breakdown'. (Long story short, Dr. Page was a scientist who invented a new superweapon, refused to sell it or reveal its secrets to the US government, was tried for treason as a result (which I am pretty sure is not how treason even works), went crazy from radioactive side-effects of his own research, also got superpowers via radioactive side-effects, faked his own death, rode a skeletal horse (because by that point, why the hell not), and tried to kill Matt and Karen before briefly coming back to his senses and saving them at the cost of his own life. Silver Age comics were weird.)
I tend to go with some kind of drug problem, possibly with some related criminal activity given that Karen heavily implies she's shot at least one person before she kills Wesley. Family issues could certainly play into that, though -- the MCU military is not above highly unethical conduct, as seen in the Hulk movies, and the stress of unfair accusations against her father (not to mention him possibly going crazy and/or vanishing) could have been one thing leading her to try drugs as a coping method, and would also be fairly easy for Ben Urich to dig up and point out as a factor reducing Karen's public credibility as a source in the Union Allied investigation.