My immediate impulse was to subvert the question as much as possible and provide a "creative" answer. I told them the best approach would be to escape the idea of a 'continuous experience' as such a notion is impractical for a company of such size and with such an expansive offering of services.
I did not get the Job.
As distant as I am now from a Google career path, I am surprised how much this question and my response come back to me.
I still hold that the attempt to unify the experience across a diverse set of services is a terrible design choice, and I sometimes see it as a huge hurdle that inevitably keeps google's apps from attaining the success of the uber-famous classic apps like delicious, twitter, and facebook. Unifying across apps means that each design is fundamentally inhibited from becoming what it needs to be, and this in the end, could kill google, as it invests millions in the unification principle.
Thoughts?