There is no shortcuts in DMOZ, almost.
But you can speed up a review of a site by submiting it to the correct category, don't try to jump up the tree two or three categories, it will get moved and the move could mean a long delay waiting for another editor review.
Try to get the tile and descriptions right, have a look at the category sites listed and imitate the style, so many sites are sent with "this is the bestest site on the web for..." and it is ibvious that the perosn suggesting the site has not bothered reading our guidelines...move to next site. But if someone has tried to get the title and decsrption right that makes it stand out and tempt the editor to look at it.
Don't submit more than once, it does over write and can delay it being reviewed and a lot of re-submissions and you could be branded a spammer.
Remember most of all that we are looking for quality, that does not mean page rank or style of the site it means unique content.
Just to add that sites offered are suggestions, some editors get most of their new sites from the suggestions pool, others never use it and only list sites they have found for themselves. We are not a listing service for web masters, there are plenty of directories who do that, Best of the Web and others. Our focus is trying to categorise unique content on the internet for the benefit of surfers. We are not interested in what page rank a site is or if a listing in DMOZ improves that or not.
Finaly it is only a hobby for us, we work in our spare time and we work at what we want to do and no one can predict how much time any editor will give in any given month or year. So that means that once a site has been offered it can be from a few days to a few years before a review. If it complies with guidelines it will be listed and if not it will be rejected. And no we don't send emails out telling people either way, sorry.
I hope that helps
edit to add
that 'almost' at the start of this post means that you can apply to edit and if you are successful there is no reason why you can't add your site, if you can edit in that category. We expect editors who list their own site to ensure fairness and list their competitors sites. If they don't do that they are removed along with their site.
I accept a few beers!!!
And of course if any editor takes money to list a site they and the site are banned for ever. Senior editors who can edit in many or all categories have worked hard to get to that position and not likely to jeopardise it for a few dollars. Those who can edit in only a few categories are hardly likely to be much help because of the limits as to where they can edit.
DMOZ is now over rated. Not googles best friend anymore. People are upset with DMOZ as it takes too long to get indexed. I wouldnt worry about putting in your sites to them.
There are a lot of other sites that have high PR, find them and add your sites to them.
The Tech FAQ?
Years ago, a DMOZ editor was being quite unkind to someone and I decided to be quite unkind to that DMOZ editor in return.
I am quite competent at being unkind, so I may be remembered at DMOZ for a long long time.
Submit Your Webmaster Related Sites to the NB Directory
I swear, by my life and my love of it, that I will never live for the sake of another man, nor ask another man to live for mine.
And it does make you wonder???
Please remember two things
1. All editors are volunteers
2. We are NOT a listing service, we are not there to try and list as many sites as are suggested to us as fast as possible. We use many sources to obtain sites, not just the suggestions list. I can tell you that it will be years before I get to look at all the sites that have been suggested in my categories, even if I ONLY work on them. But I also have to deal with updates, sites going 404 etc and I want to find some sites my way, it is after all my hobby and my spare time. All we get paid often is insults. If you don't like what is listed, then push the "I want to be an editor" button, pass the tests and then help us by spending a few hours every day editing. It is great fun.
Actually it is not, I've been an editor, and most editors just don't give a damn about DMOZ.