Reflection was actually my first thought too - glass shows reflections when there's a substantial difference in the amount of light on both sides (i.e. when one side is light and the other dark, the side with more light will start reflecting). So, if the lights are off outside of the tank but you have moonlighting or something on the inside of the tank, it's possible that the amount of light in the tank is enough to cause reflections on the glass.
I have no idea if this is the problem for your tank, but if it is you could just light up the dark side and the reflection would go away, or you could block the light from hitting the light side and that should get rid of the reflection as well. For it being lighter in the tank and darker out of it, I've seen someone put a white piece of paper on the outside of the their tank to reduce the light difference inside vs. outside, and that successfully eliminated the reflection they were getting; some other suggestions include blocking the light from hitting the glass inside, or putting little LED's around the outside to light it out and decrease the difference in light.
Regardless of if this is what's causing problems for you or not, though, I hope you're able to figure out what's wrong soon - best of luck!