I know people that are on their 4th Kalamar campaign, and still have not utilized all the known world. I have no idea what I would do with even more land mapped out. (Mark, how many square miles is Tellene?)
As far as the people and the economy are concerned, there *is* no rest of the world.
And forget some unfulfilling drawing, they have a full fledged Atlas. Talk about great informative detail.
The timeline is static. You don't have the FR/Shadowrun type of situation where you have to be careful about which modules you run, since the world has drastically changed between them.
The world just makes sense. The geography, the population sizes, the political settings, etc.
I really can't think of a better setting for a beginning DM. In fact, I will be starting my first campaign in about 3 weeks...and you can bet it will be in Kalamar.
Really, go to their website and check out some of the info they have. The Atlas is great, the campaign setting is very informative (though it is textbookish, so some may not like to cover to cover it.), the monster book cares as much about how the creature lives, and where, as its HD and attacks, and it has, by far, the best DM screen I have ever seen.
Oh, my current favorite part, is the player primer, where it give info about what you may know regarding other parts of the world.
However, all you need to run in KoK, is the campaign book. and only need to skim the parts you want. If you are looking for others, the Atlas, players handbook, and then some of the location books (geanevue, Loona, etc.) would probably work well.
And Mark was a bit misleading

, the 'crunch' he referred to is there, but it isn't necessary crunch, it is literally one new weapon, or one new type of armor, etc. It is crunch only added for flavor, not required for the campaign.
For your DM's sake, I really suggest he spends some time on the website to get a feel for the setting. Oh, and about half of their modules are on sale for $5. The critically acclaimed Coin Trilogy can be had for about $20 total. (three modules linked together, I know many that have DM'd it multiple times.)
Good luck, and I hope you have fun in whatever setting you choose.