As others point out, there are arbitrary-precision software packages that wouldn't suffer any numerical inaccuracy. That is what you'd use in a competently designed system.
But, if you insist on using floating point numbers, there is one significant effect that would occur- it would be possible to specify nearby locations more accurately than far locations. This normally doesn't matter because our earth is relatively small, numerically speaking. But in the realm of space the distances become very large indeed.
As a loose explanation, floating point numbers have a limited number of precise digits due to the way they are represented in a machine. In one common format (the 32-bit, IEEE double precision floating point number), you have about 7 significant digits of precision. Regardless of whether you're representing a large or small number, you only have 7 digits to do it in. For example, the numbers 1.234567 and 123456.7 both have the same numerical precision (seven digits after the most significant).
Suppose you are counting kilometers directly. Nearby locations can be specified with great accuracy:
"Move 0.001 KM away from the planet" would be equivalent to moving one meter, or
"Move 0.000001 KM toward the ship" would be equivalent to moving one millimeter
However, far locations can only be specified very coarsely. If you say:
"Move 1000000 KM along this vector" then the last precise digit is the 1KM place. 204
You can't say "Move 1000000.001 KM", as your maximum precision at this point is now 1KM. Likewise, if you say "Move 1,000,000,000 KM in that direction" your maximum precision is now 1,000KM. You can specify the following two locations accurately, but nothing in between:
1,000,000,000 KM and 1,000,001,000 KM
Astronomic distances are very large. In order to "jump to" a star system you need to get within a few hundred thousand KM. Our closest nearby galaxy (Andromeda) is 2.4*10^19 KM away, with 7 digits of precision you can only discriminate plus or minus 10^12 KM (a trillion KM). With a double precision, 64-bit IEEE format you've got about 16 digits of precision, so you can specify locations plus or minus 10^3 KM (a thousand KM) in Andromeda. Again, that happens to be the closest galaxy.
Consider what happens when precision breaks down. If you're plus or minus 100,000 KM then, to avoid jumping into a planet, you need your jump target at least 100,000 KM away from the planet surface, which might be as much as 200,000 KM if you round the other way. If it's critical to be close to the planet when you jump, you need your origin point to be closer to the destination. Hence you would have to jump somewhere near the solar system, and then you would jump to the planet.
You can come up for your own explanation of why that's good or bad for economics or military engagements or what have you. 921