Second to last Holiday iPad app question! Tricks of the trade for holiday entertaining -- send them here!
Mingle while they are eating? Do you mean before and after dinner or maybe conversation while everyone is eating. A little confused by the question.
You could play a version of fire drill where everyone has to trade places with another person?
If you are looking for a conversation prompt, try a variation of "six degrees of separation"...
This may not be what you're looking for, as I'm not big of formal tactics. (Just me I'm sure, but that usually reminds me of being at a child's birthday party.) I think a lot of it is who you invite. Unless it's an everyone-you-know type affair, or you're compelled to have a specific group, make sure to include some guests who are naturally outgoing. I often invite one old friend, not only because I adore her, but because (as she and I joke) she's 'socially promiscuous'; if she gets on an elevator full of strangers, she knows their grandmothers' maiden names before she gets off. She's a subtle Julie, the Cruise Director at parties too. (Only the ancient will get that ref.) Also, try not to plan a menu that chains you to the stove, out of the mix, for most of the party - so you can participate in getting the conversation flowing. (A good party isn't about a 97-step entree.) If a guest is very shy - and it's someone you feel comfortable asking - have him/her help with drinks; point out mutual acquaintances/interests; tell a funny story about someone there; whatever lubricates the initial mingling. And one pet peeve re: what not to do: of course it's good to invite people who share interests, but unless it's a professionally-related gathering, don't make it all lawyers, or teachers, or architects, or circus performers...if that's the only commonality, the conversation can quickly become nothing but shop talk. Which, for me, is not so much fun. (In other news: we really need a way to break an answer into paragraphs here - look at this block o' words!)
I once read an article on this-ways to keep the conversation going at dinner parties. It actually states to invite people with different interests....and not only that, but to separate couples so that you're forced to speak to the individual next to you. I've never tried this method, but it's something to consider.
Small plates, lots of wine, and hide the chairs.