Why is spying on the UN worrisome? Countries spy on each other, because countries lie to each other all the time. It's how countries find out what's really happening as opposed to what's said publicly.
The compromised UN is effectively a body for representing and legitimizing the wishes of the cabal of US allies as if they were the actual consensus of all UN member states.
[1] But it is still not possible for any nation to be more effective at spying than the US, given the UN's location.