One problem is defining what "intruding on others' happiness too much" means - it's not obvious how to derive from this principle the hours when making loud noises within city limits is OK, or what about necrophilia in public, or pollution, etc. Almost anything I do might make someone very unhappy and I'm not sure what philosophical principle can be used to distinguish cases where I should stop doing it from cases where I should be able to reply "toughski shitski."

Another problem is whether it's OK to require a thirsty person in a desert to give up all their assets in exchange for water, and whether it's OK for the thirsty person to knock you out and take the water in response; most people would side with the thirsty guy for what I think are very good reasons in terms of the practical implications while objectivists would not.