Almost zero. Only the last few people on the plane have trouble getting seats together. And even then they can usually move people around to get a parent and child to sit together. And while the odds aren't exactly zero, they aren't zero on other airlines either as they will sometimes have to move people out of reserved seats.
I'm a huge SW fan, been a frequent flier for years, and to be honest, I have no idea what early check-in is. But as long as you check in close to 24-hours in advance, you'll be fine.