Neelix doesn't give up his comm badge when he leaves for good. It wouldn't really work from that afar, but, does make a nice souvenir.
Neelix says the ceremony commemorates the 315 anniversary of Vulcan's first contact with Earth. This would place the episode in April 2378. However, the common method for dating episodes holds that the entirety of Voyager's seventh season takes place in 2377.
The Talaxian colonists discuss returning to Talax even though it would be tens of thousands of light-years away (based on the distance Voyager has travelled since visiting the Talaxian system in "Jetrel") and would take decades for them to reach.