The Background
I work with a LOT of non-native English speakers. As such, miscommunications are a daily occurrence. I've noticed that sometimes when they don't understand something, they'll just nod and smile, or smile and say "yeah." Whether this happens because they deem the act of asking for clarification to not be worth it given the conversation or they're too embarrassed to admit they don't know, I'm not sure of.
The Problem
Since I'm on friendly terms with many of these people, I'll joke with them and our conversations will carry lighter tones. This usually results in me dropping my guard and not always remembering to enunciate and talk as slowly as I need to. My issue comes when I ask a work related question or a question that I need answered and they nod and smile.
In my experience, re-asking the question or making it clear that I asked a question results in embarrassment for the other party. I understand that I need to better enunciate and talk slower around these people, but realistically I can't always remember to.
The Question
Once I'm in a situation where I've asked a question and gotten a nod and smile, how can I get the answer I need while minimizing embarrassment for the nod-and-smiler?
Note: I've tagged this United States, but I'd be interested to hear if other cultures have their own ways of dealing with this!