Is it okay to cover food in the fridge with paper plates?
Ideally you should get airtight containers, but failing that, plastic wrap is indeed a lot better than just covering with a plate.

As you say, you'll tend to get more smells mixing around in the fridge if things aren't airtight, and it's something that can kind of build up over time, with the interior of the fridge just taking on a mix of all the smells. (Fridges can eventually smell weird even if you're not doing this.)

It's also not generally as good for the food; it'll dry out faster. Might not be an issue for everything, but sometimes it can be pretty obvious. It may also get contaminated a little more easily and spoil faster, but that's a little random, hard to say anything specific about time periods.