All of my shapes on my globe are outlined in white even though I do not have a stroke selected and there is not a second stroke showing up in the appearance pallete.
How can I get rid of the white outline of all the land masses?
Here's my view:
The continent's, aren't exactly against the water. There is a small gap in between the water and the continents. As the water is a plain color. You could make a circle and put it behind the continents. This will get rid of the whitespace.
So your layers will be like this:
I hope this helps you out!
My guess is this stroke is actually a compound shape under or around the green areas.
I have 2 possible solutions that may work even if my above assumption is wrong:
Select any of those strokes with the white mouse tool (A). Then, go to your layers window and scroll to find the selected piece (should be marked with a full radio button). That way you will be able to see what exactly is going on there - could be mask/group/compound path/regular shape/etc. Try hiding that specific piece and see if the stroke gets hidden as well, as well as if anything is attached to it.
Double click the (amazing) magic wand selection tool (W) and change the settings to find only stroke color. Then, create any random shape with a white stroke somewhere around and press it with the tool. All other similar stroked shapes will be selected to be easily removed. You can try it with only fill color option selected also, in-case the "stroke" is actually a fill. Just make sure nothing else you actually need is erased (or undo at worse case ;)).
Using illustrator's outline view (CTRL/CMD + Y) can help recognizing such issues as well even before actually doing anything! I personally use it ALL the time (for other reasons too).
Hope that helps