Seems to be broken. God this game is sooo unfinished.

Could you elaborate? What's broken about it? Did you report is as a bug?

Well I got the Salvaged Relationships in the Neutral Zone.
Says Win any War Zone.

There's only one War Zone map, which is Borg Hunt. I wont the map. But the quest didnt complete. No rewards for playing either.

This also happened to my group. We tried it several times but it never showed we finished it. I don't think it is broken though, I just think we weren't doing something right to "win".

Though I have seen the message stating the Federation has won, I never received credit.

One player said you had to complete it in a certain amount of time for the credit to count, but have not been able to verify this.

Yes, it is broken, does not complete. ANd yes, bug reported it.

It said we completed the map. When you select war out it says Mission Completed. Are you sure you want to warp.

I don't know if this will apply but I've heard that some missions will only complete if you Hail Starfleet before you warp out. Give it a try.