I was thinking that maybe qualifying for an apartment isn't the only reason you want to improve your credit score. There are debt counseling services that are free, but none that I know of for just improving your credit score. (you r credit score does improve when you pay your debts but that's only one piece of it.)
If you have items on your credit report that you dispute, I'd suggest you contact Jeff Sipes at Blue Water Credit at 916 315 9190. He's one of the few companies that I've seen actually do what they say they will when promising to improve your credit. In addition, I'd read the book 'the Richest Man in Babylon' which outlines the best plan to properly handle your finances. Last, I'd subscribe to the Clark Howard website at http://www.clarkhoward.com.
He's a consumer advocate and has all kinds of good ideas on keepng your credit score maximized and manage your finances properly..
I think educating yourself on the proper way to handle your finances might help in assuring a landlord that you appreciate that you wold be a good risk in paying your rent every month, and on time.