DMOZ has never been, is not, will never be, a listing service for webmasters. It is not our job, is not any part of our concept, to provide in any way shape or form a listing service for webmasters. If anything we are the anti-Christ of listing services for webmasters. We do not exist so webmasters can send us their sites to review and list so webmasters can promote their sites, increase their Google Page Rank, sell their wares, show off to their friends what brilliant web marketing experts they are.
So what are we?
We are a bunch of unpaid volunteers who spend their spare time working on a project to catalog all the unique content on the Internet that we can find. We search the search engines, we write down URLs from the back of buses, we ask whether our dentist has a website. We trawl through pages of links on personal websites and on other directories.
And we invite members of the public to help us with our little project by sending us their suggestions. It is called the Suggest URL feature. It can be the results of their travels around the Internet, something they have seen on the back of a bus, their dentist's website. Or it can be their own site.
We take all the stuff we have found ourselves, and everything suggested to us by the public, and when we have some spare time we look through it at our own pace, listing some, rejecting others, saving the rest for the next time.
How effective can this project be when it takes a minimum of several months for approval of a site?
The project is extremely effective because as indicated above we are not in the game of approving sites as a listing service is. True quality and originality in areas we believe of most use to the users we serve always stands out and gets priority attention. Sadly it is not that common as affiliate marketing sites swamp the Internet. In many categories the wait for a review can be as little as a few hours - tends to be those categories that attract those brilliant sites I mentioned.
I was rejected for some unknown reason
I won't speculate because I can't possibly know any more about that than you. But you seem to have a fundamentally wrong idea of what DMOZ is about. Though you aren't alone.
There are several sites in the category that I submitted to that are invalid links.
Point us at them, we always welcome more eyes working on these things (especially me). Generally completely dead links are automatically weeded at regular intervals.