When should your team or organization talk about your values and mission?
Every chance you get.
I believe that time should be given in every meeting to 'values and mission.' It might not be an agenda item but there should be intentionality to intertwine and evaluate all discussions around values and mission.
Dan Cathy, the CEO of Chick-fil-A has gathered a group of items he keeps in a "Leadership Tool Kit." One of the items is a railroad spike. He explains that the railroad spike represents a company's core values and they are what secures that the organization stays on track.
I will take it one more step:
When you look at a train track you don't just see four or five spikes holding down the track but hundreds and even thousands. The 
spikes are not different but all look the same. The repetition of the spikes is what keeps the track down. Let's look at if from an organization's or team's perspective. A team or organization does not have hundreds or thousands of values, often just a few maybe four or five. Yet it is these values that keep the team on track, and the team needs the values all along the way. It's the repetition of the values that secures safe productive passage to the destination.
In the team meetings that I lead:
We examine our own values
We look at our action items, projects and goals and their relationship to values and mission.
We often look at the values and missions of other like organizations to see what we can learn.
These discussions help us evaluate our beliefs and therefore they help us mold and further define our own values.
The mistake of a leader or organization is not talking about values too often, but the failure to repeat values and mission.
How often do you hear, repeat or discuss your organizations core values?