A lot of mistakes came out of being independent. The mass slaughter of Indians not being the least of them. Slavery lasting a fair bit longer than it would have otherwise. The civil war (which we sadly lost). Not to mention if we stayed out of the WWI, Europe would have reached some better settlements and peace treaties, meaning Germany and Italy would have remained traditional monarchies. With a Russian Czar and a German and Austrian Kaiser in place, it would have been almost impossible for the Bolsheviks to seize power in Russia, and in reaction to a growing communist threat in Western Europe, for the Fascists and National Socialists to do the same in Italy and Germany (especially since they couldn't be elected into power, since monarchy != democracy), preventing WWII and the slaughter of juice. We'd also probably have remained on a gold standard, meaning we wouldn't have the economic crisis that we have now.
I think independence was a wise move.