Click the Victory Conditions button in the upper right corner (looks like a fist). It will show you how many parts you have built, and how many parts the civilization closest to completion (other than you) has built.
I discovered how to do this tonight. Go into the info screen (the one with the score and power graphs, I think it's F9) and click on Top 5 Cities/Wonders. On the right is a list of wonders. In the popup menu above the list, pick Projects, and it will list all the projects completed by all the civs. You'll have to add things up yourself, but you can figure out how far along each civ is toward completing the space race.
The further along the project is (spacerace) the more costly it is to sabotage it. There are also risks of getting caught and can be fairly high. I have in some of my games had to spend 3000 gold and ended up failing. If the spy gets caught you will get a negative with the civ that caught her.
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