Calculating a planet's mass & gravitational pull

[Suicide Junkie]

Differing densities at various depths does not affect the calculation, assuming that at any particular depth, the density is the same all the way around the planet.
If the density is not the same (ocean water vs rock, say) it still only has a small effect, which is swamped by the effect of the 1000's of km of rock below it.

Distance from the planet surface has the biggest effect.
If you are on top of a mountain, the gravity is lower. While there is a bit more mass directly below you, the 1/r² decrease hits much harder.

However, its still a fraction of a percent change.

You'd need something with an irregular shape, like an asteroid to get decent changes in gravity, but then the gravity is so low to begin with, it really dosen't matter.

Stuff with higher gravity smushes itself into an ovoid ball, and the approximations apply.