If you go through Dmoz, you will see it is declared "..it may take several weeks or more.." depending on the various criterion. Actually Dmoz listing can take up to 6 months or more. It also presents you the worst possibility, which is not being listed in Dmoz. But being an experienced Dmoz lister, I will share some secret tips which will guarantee permanent listing.
I) Many websites goes offline due to various reasons. These websites are called "Dead website". Every directory (including Dmoz) in internet contain dead websites. If you are lucky enough, you can can find one within your preferred category. After finding, you can ask the editor to replace the dead link with your's link. This is one of the proven secrets of fast dmoz listing.
II) Create a free account in forum sites like digitalpoint, resouce-zone(Official forum of Dmoz). Editors of Dmoz frequently visits these websites and many of them has an account. After submitting your site to dmoz, announce in those forum. Your chance of quick review will increase and waiting time will be shorten.
III) Find the appropriate category. Go as deep as you can while selecting category. Because deepest category does not have steep competition.
IV) Many webmasters commits a common mistake like submitting their website to exact same folder to competitors. It is very inefficient, avoid it.
V) Last but most important; never ever submit your link twice or more within short period of time. By dong so, your waiting time for review can increase to infinity.
VI) Take note of the 'Last Update' date mark at the bottom. If the category, you selected to submit has not been modified for a long time then there is no point submitting. There may not be any Editor in that category.