While there may be some errors due to accuracy over time, as Physics_Hacker suggested, these certainly wouldn't be enough to throw off the Moon that significantly in just a few simulated days.
I checked with our team and it appears our database information for the planets are correct in the "Now & Real Time" sim, but the Earth's Moon specifically seems to have an error somewhere that is setting its position in its orbit about a quarter farther than it should. So this is an error on our part, and not a fault of the simulation itself, or the fact that it is simulated. We'll look into this! Thanks for pointing it out.
Edit: We determined that all of the major moons are 90 degrees (1/4 of the orbit) farther than they should be, at least in that sim. We're looking into this to figure out where this error is happening. Thanks again for pointing it out. We appreciate having users who pay close attention!