If you were on a perfectly flat plane

[CombustionMan]

..that went an infinite distance in all directions:
What would it look like?
Would you technically be able to see all (or a lot) of it? (speed of light permitting)

It's just a question that has been bugging me for a while.

 

[Curl]

No, the angle will be so small that your eyeball cannot resolve the edge. It will look like the ocean.

 

[PolarisNorth]

You said there is infinite distance in all directions so in technical terms, you can't see "all" of it because infinite is going on forever with no boundaries and because it is infinite, there is nothing else past the plains so you will only see a horizon where the ground seems to meet the sky.

If you are in an infinite plain with no plants, then no matter where you stand and in what direction you stand, your view will always be the same. I think it would be similar to how a desert plain looks, like in this picture:
http://murmeli.files.wordpress.com/2007/03/plain-desert.jpg

 

[Hootenanny]

And no matter how far you moved, you would always be at the centre of the plane

 

[askAphysicist]

It's the same issue you have when looking at anything: the further you look, the wider your field of view gets, but the smaller the individual things you see appear. If you'd imagine the plane you were standing on was painted with a black grid on it, all the lines would converge at the horizon until it's all just black for you.