Can we determine, with respect to the centre of our galaxy, what the time dilation is on the surface of the earth. This would mean determining a value for the mass of the galaxy with the dark matter element included. Then calculating the potential that the earth is at. I was considering this with respect to external galaxies. From our perspective do we view the universe as running faster than it actually is due to our time being time dilated. This would skew our measurements of expansion.

For your intended purpose ( how it effects observations of distant galaxies), you don't want the Earth's gravitational potential with respect to the our galaxy's center but with respect to some far distant observer.   For that, you can get a rough estimate from our distance from the center of the galaxy and the mass of that part of the galaxy closer to the center than we are.  This comes out to a time dilation of 1 part in 624,000 due to gravitational potential.   However, this would be mitigated some by the fact that the Sun has a orbital velocity with respect to the Galaxy's center,  which accounts for about 1 part in 3.5 million. ( if we are viewing some distant point in the universe, we would see its clock run fast due to the relative gravitational potential, but run slow due to our  relative velocity difference.
So how would this effect our observation of the Universe?  Consider our nearest large neighbor, the Andromeda galaxy. We measure its radial velocity as being 301 ±1 km/sec.  Which means we can only measure it to ab accuracy of 1 part in 301.    In other words, the excepted error bar in our observation far exceed any correction required to account for time dilation.