Bike rests on brake cable while racked
Could this cause me to have brake problems


Yes: The weight of your bike will pinch the cable and slowly cause the cable to lose its structural integrity and become damaged: They are designed to take stress along them (tensile strength), not laterally (shear strength)... hence how they can withstand huge amounts of force from braking yet can easily be cut with cable cutters by most healthy people.


  what can I do to mitigate this?


Don't pinch the brake/shifter cables between anything. If your rack pinches them, adjust the rack or get a new one.