What is this url: http://editors.dmoz.org/editors/editunrev2.cgi Is this a review page? Additionally, if a dmoz editor only gives your site 38 seconds, does that mean that you can forget inclusion?
The URL you post is for editor login (password required) I didn't understand you're question about 38 seconds, sorry.
basically I offer a service. But the editor only checked out my terms of use and privacy policy, but didn't check out the free service by registering. Also: If I am included after this review, how long will it take for my link to become active?
On that basis it is unlikely the site was accepted, an editor would check the content pages. If this requires registration many editors are unlikely to pursue further review and will leave the site for another editor willing to register. Probably for all time. You can provide a guest username and password using [square brackets] when you submit the description and this will encourage the editor to undertake a review. You can submit an update to provide this information if you didn't originally.