I own a Nalgene water bottle (one of the camping "unbreakable" ones) that is not suppost to retain smells and tastes. I put grape juice in it and now everything I put in it tastes slightly of grape and it's not going away. What can I do to get rid of this problem?

You can always try rinsing it with bleach, which will not only get rid of the taste, but disinfect it as well. Of course, you want to rinse it thorougly with water afterwards to get rid of the bleach. Also, it may taste very faintly like bleach after that, but it shouldn't be very noticeable, especially if you rinse it thoroughly with hot water.

Rinse it with warm water, a bit of detergent and table salt. AND: use your hands while washing the bottle, not cloth which you use to wipe other pots n pans(If you do so). This ensures that no foul smell is left behind.

Happy Rinsing ,
Pin~Jinx

You could also try a mixture of baking soda and water. Baking soda is used in refrigerators to remove odors, and help prevent food/beverages from picking up bad tastes from smelly foods.
I guess I wouldn't try bleach if it might leave a bleachy taste, since that is what you are trying to avoid.
Does this bottle come with some sort of guarantee?
If so, I'd write a letter to the company.