What are some applicable problems with the correct usage of G? In some fields of astrophysics, where distances are measured in parsecs (pc), velocities in kilometers per second (km/s) and masses in solar units (), it is useful to express G as approximately 4.302 x 10^-3 pc M^-1 (km/s)^2 ...
Is G not approximately 6.67 x 10^-11 N(m/kg)^2? Any reasonable explanation would be appreciated.
I think one of the reasons for using different units is how you take the measurements for the other variables in the equation.

For example, let's say you have two marbles, and you want to calculate the gravitational force between them (not a lot!). You place them a certain distance apart, and measure it with your meter stick. You find the distance between them to be $0.146 \text{ meters}$. Now you weigh them, and find their masses to be $0.00156 \text{ kilograms}$ apiece. You decide to use the value of $G$ with units including meters and kilograms.

Now let's say you have two stars far, far away. You take measurements based on parallax and find that they're roughly $35,400 \text{ light-years}$ away from each other. Your instruments can't measure this to any greater accuracy. You measure their masses by calculating how much they deflect light, and come up with a figure of $10 \text { solar masses}$ apiece. You therefore decide to use some form of $G$ that, for some reason, has solar masses and light-years as some of its units.

Basically, you choose different forms of a constant depending on the units you're able to measure with your instruments. You won't be able to figure out exactly how many meters your stars are apart from each other, but you can figure out just about how many light-years apart they are, with less than a light-year of uncertainty.