Clashing expectations are what most consistently derail any team, and especially a culturally diverse team. So if you take the time to "define" the goal carefully upfront, you've addressed one of the most difficult and important parts of the innovative process.
Perspective taking is taking on the perspective of others. It's what we do anytime we buy a gift for someone else ("What would they like?"). So it means breaking the golden rule ("Treat others the way you want to be treated") and instead, acknowledges that others may not want what you want.
Even an organization that doesn't do much work internationally will benefit from a culturally intelligent strategy to innovation. Working across different generations, business units, regions, and functions are all factors that can also influence the innovation process.
When you jump on a city bus or roam the streets off the major thoroughfares you'll quickly learn that we have as many differences as similarities. And therein lie the greatest opportunities for innovation - our different ways of viewing the world and coming up with solutions!
The very ability to empathize with a user requires that I have an understanding of that user's value and needs. This is what leads to many product fails. The individuals developing the innovation don't actually use it.
Smaller companies are often more homogenous. Don't simply increase your diversity because of the social pressure to do so. Instead, realize that hiring a more diverse team will give you a whole new repertoires of innovative ideas. And then develop a strategy for effectively using the diversity of your team.
The distraction, particularly of technology, impedes the innovative process. And when you add to that the distraction of working with colleagues who are in different time zones and/or who have a different approach to urgency and distraction, the potential for losing focus is abundant.