Even if you're just doing a 2-body problem around the moon you'll get wildly wrong orbits over a timespan of just months if you treat the moon as a point mass (the way that's relatively safe to do with Earth, in comparison). Lunar mascons are so strong you can't even rely on a plumbob to point straight down if you want just tenth-of-a-degree accuracy. These perturbations are so severe there are only effectively only four (instead of 90) stable inclinations for low lunar orbits.
Literally every body in the solar system acts on every other body at all times. All asteroids in the asteroid belt are perturbed by Mars and Jupiter, right? Except if you recognize the need to include Mars in calculating their trajectories, you need immediately to at least also account for the 4 Gallilean moons, who sum to about the same mass as Mars, and now you have a 7-body problem. You won't get correct results on trajectories of Earth approaches if you discount the mass of our moon, nor if you discount the rest of the asteroid belt (4% of our moon's mass)... etc.
Literally every body in the solar system acts on every other body at all times. All asteroids in the asteroid belt are perturbed by Mars and Jupiter, right? Except if you recognize the need to include Mars in calculating their trajectories, you need immediately to at least also account for the 4 Gallilean moons, who sum to about the same mass as Mars, and now you have a 7-body problem. You won't get correct results on trajectories of Earth approaches if you discount the mass of our moon, nor if you discount the rest of the asteroid belt (4% of our moon's mass)... etc.