I had a very similar problem a few days ago..and I did some research
Nail polish remover will work only if it contains acetone.
You can get a bottle of acetone from your local hardware store and pour some on the glue, wait, then blot it off with a towel. However, always test the acetone on an inconspicuous spot first because it's very strong and may damage your costume!
I've heard glass cleaners such as Windex also work in the same manner. I just went to a hardware store and bought a bottle of liquid adhesive remover and it worked pretty well. Remember to always BLOT at the glue, not RUB...or you risk getting the glue embedded into the fabric even more so.
But if you don't want to use chemicals, you can place the glue spot on top of a paper towel or piece of cloth and run an iron over the garment until the glue melts. The towel/cloth will absorb some of the melted glue; you'll just need to repeat the process until all the glue is gone (remember to move the glue spot over a clean part of the towel/cloth each time).
I've also read something about making a solution of 1 quart warm water, 1 tablespoon white vinegar, and 1 tsp laundry/kitchen detergent and soaking the garment in it for 15 mins, then blotting at the glue spot and throw it into the washing machine. (Obviously, this method doesn't work if your costume can't be machine washed or drowned in a solution)
I've never tried this but you can also freeze your costume in the freezer and then quickly scrape off the frozen glue with a dull knife.