Can Vatican really be considered a sovereign state?

The UN recognizes it as an official state, but...
To be honest, isn't it not a sovereign state in the true sense of the word?
It doesn't even seem to be as much as an Italian colony...
It doesn't even look like the Pope has the power
to directly try people who commit crimes within the Vatican.
And don't even get me started on the military...
Shouldn't countries like the Vatican, Monaco, and Andorra
not be counted as actual countries?