I wouldn't worry about that at all. They are both still doing their job and when combined should results in better results because of their different mechanisms of action. Moreover, I don't think people should be on DNP enough time for these sort of things to really come into the equation. Now HGH and thyroid are a bit different due the time most spend on HGH so if someone wants to supplement with t4 (and t3) they could if wanting to get completely peeled. I could probably benefit from that because HGH makes me extremely tired but I usually stay away from thyroid meds and I have never needed them medically.
Now the one issue that could arise from running both are simply side effects if you're everything like me. HGH and DNP are the two things that have the biggest impact on my energy levels. Again though the length of DNP usage is a prime reason I will run both together because it simply means having very little energy for 2-3 weeks which is not the end of the world. The dose is also a very important part of the equation and that's why I tend to stick to 1 cap of our DNP and 2.5IU HGH daily to combat potential side effects. I started HGH the other week but never run it everyday but even if I had I wouldn't worry about adding DNP to the equation.
A little update and as posted I took 2 caps of DNP yesterday to load it in and I was fine last night (a little heat and felt good) but today my energy levels are non existent. I had a decent sleep as well but even walking my dog is a struggle. I will carry on with 1 cap per day for approx 6 days with a very restricted (but high protein) diet and that will finish things off nicely. I am relaxing now and just waiting for any sort of physical/mental boost before I go to the gym