Every employee of the United Nations has diplomatic immunity. With D.I., is there ANY crime that they could be arrested for? They've gotten away with rape and murder in 3rd world countries, but would it fly if one went on a murder spree in New York City?

So long as diplomatic immunity is place, the answer is no. But you have to look at DI in context. The immunity comes from the constructive fact that the diplomat is physically on foreign soil, but bound by the laws of his homeland. Thus, he is immune to foreign prosecution but not to domestic prosecution. Moreover, the home country can always waive immunity.

For example, if a U.S. diplomat in the UK went on a murder spree, could he be prosecuted in the U.K.? The answer is no, so long as DI applied. But chances are the diplomat would be prosecuted. How is this so? Well, first, the US would likely waive DI and allow the diplomat to be tried in the UK. Second, if not that, the U.S. would prosecute the diplomat in the US.

Well, first of all, not every employee of the United Nations has diplomatic immunity.

Also, as happened in the past, the Secretary General has the power to cancel the diplomatic immunity, which he will do if one of those holding it commits a crime that is of considerable gravity. This happened a couple of years ago when the police in the US arrested a man for some kind of fraud type crime, and they let the arrest and charges go ahead.

So, if someone who did have immunity went on a crime spree, he probably would not get away with it. Diplomatic Immunity is not unconditional, nor is it a license to commit crime. It lets people 'get away' with actions which they would perhaps not realise were not permissible in that particular country. That clearly doesn't apply to murder.

Basically, it is to help them work and carry out their duties, rather than a 'license to do as they please'. It does get abused, though. You are right on the money with that. Both in minor ways, and big ways.

i am sure you are hurt because of that, right?
i feel the same, believe me.

Every employee? I know a translator who works there and I do not believe she has diplomatic immunity.

According to various TV shows and movies, yes.