Offset in a comparator's input
I don't know what weird results you are getting, it could be that you didn't check the input common range. 



The input common mode voltage (average voltage of the inputs) has to be about 0.2V above the negative rail.

As pointed out by Carloc, a detailed description of the behavior of the comparator over the input voltage range can be found in the datasheet. I've added Carloc's screenshot below