Yes, I would say that flat+/-25% is indeed a tough target to reach, for a beginner. There will be several things that contribute to a lack of flat response. One is your receiver circuit, but you have control of that and can try hard to make it broad and flat. The next is your antenna, which will not be flat.
The third problem is that the field you are trying to measure is not supposed to be flat. If you radiate a "flat" amount of power from a radiator that has a "flat" frequency response, then the field strength you measure at a fixed distance will not be flat, but should decline in strength as the frequency goes up. This is in theory anyways.
So, if your meter was perfect and ideal, it should show a declining field strength with an increasing frequency.
Well, don't let that bother you. Just try to build something that is sensitive and if you include a microprocessor to read the voltage and display the result, you can include a correction table within a program that allows you to calibrate your unit and cancel out all the errors. Neat eh?
I'd like to add that +/-25% error in reading a power density is an error of only about +1/-1.25 dB. In the world of antennas and field strength measurement, this is actually pretty good. I think that if you achieve +/-5 dB error you are doing ok.