The collateral damage includes political fallout, damage to bilateral relations with friendly countries, and an increase in the risk of being treated as a pariah.
Are you talking about the collateral damage of (e.g.) invading Iraq or Afghanistan? Or are you talking about the collateral damage of using hit squads to take out terrorist leaders?
exactly. Is it worse in the eyes of the world to say that you're 'fighting a war on terror' and invade a country or secretly kill high-ranking enemy officials for years before finally getting caught?
The second is more expedient, but if you kill the wrong person at the wrong time, you can probably cause yourself a lot more harm than good. Imagine if the US killed Saddam Hussein by poisoning his breakfast!