I'm hosting a dinner party in which one couple is gluten-free & paleo, while the other couple is vegetarian. Help!

Well paleos, to my knowledge, eat meat, so if you wanted to go ahead with a non-veg main, you could do that while making sure your sides were good enough to stand on their own. I'm a veg and I never mind eating a bunch of sides. I actually often prefer it. Alternatively, if both groups eat fish or eggs, you can focus the meal around either. I think frittatas can be fun an unexpected even for dinner.

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Try a Cauliflower couscous. http://food52.com/recipes/14493-cauliflower-couscous
Serve topped with a eggplant and veggie tagine as one option and a lamb tagine as another option.

Oh, yeah-- dairy is another thing to ask your paleo friend about. Some say "no" altogether, some say "no" to pasteurized but "yes" to raw. Others don't really care. Obviously, the above was for a semi-paleo who didn't care about dairy.

Find out just how "paleo" your paleo friends are. Some allow rice; some don't (and sometimes it is no white rice but brown okay). If so, you have lots of options. Rice noodles or rice itself can make a lovely casserole that is gluten-free, paleo (see above) and vegetarian. With the vegetarian, find out if fish and eggs are allowed. Had a similar situation awhile back where rice and fish were both okay, so made a "white" lasagne (beauchamel instead of bolognese sauce) with rice noodles, smoked salmon and spinach (sorry - don't have a recipe to share -- simply started with a traditional lasagne recipe to give me ratios/quantities and substituted madly). Another option (assuming rice is allowed) is to go Asian inspired stir fry -- lots of wonderful veggies, with special (take on fried) rice on the side. Or think a lovely, winter vegetable stew made with vegetable broth, perhaps thickened with some quinoa (BTW, cut up sweet potatoes add a lovely flavor to these stews). Search the recipes here on food52 for "Vegetarian" for even more inspiration.

Wow, that's rough! What about something like socca pancakes with a ratatouille or mushroom ragout and a lovely egg on top?

That's a tough combination. Perhaps you could make a crustless quiche or frittata--and you can use mushrooms for a bit of meatiness. For a salad, you can used mixed greens, roasted beets, orange, goat cheese, perhaps some dates and avocado. Dessert is easy--- chocolate pudding made with heavy cream and dark, dark chocolate. I have the recipe if you need it.

You can make kale chips and dip, depend what kind of vegetarian you can make salmon cakes http://food52.com/recipes/11937-sweet-potato-salmon-cakes-with-chipotle-mayo, Deviled eggs, a citrus fruit salad