@1: As you already know, there is a link "update listing" at the top right of the categories where you can submit any changes you like. Of course they will have to be checked by an editor before going live. We all don't like people hijacking listings by changing the URL to something totally different, do we? Apart from that, there is a well defined way a server has to report that a link is 404, which has nothing to do with page layout whatsoever, only with a header field. If hosting companies choose to give their clients a reduced service by not reporting such links correctly, well, change the hosting company.
(I can imagine you saying: "But the person that has submitted the site should be able to..." - Definitely no. We really don't want those adult webmasters to submit random sites and change the URL once they are listed. There is no way to assure a change is valid but make an editor look at the site.)
@2: All categories can be edited from a) listed editors b) all editors listed in parent categories up to the top and c) quite a lot of editors with directorywide editing permissions.
Until recently, update requests did not stand out, so one had to look for them by hand. Since a short while now, we are able to spot them much easier. So you can expect better handling in the future, once people are used to that system. I already processed update requests in large areas that I rarely ever edit in, large areas that are now "update-request-free".
@3: Yes they do, thats neither new nor something we can change. If you spot such URLs, submit update requests so that editors know about them. If you spot a certain scheme that might help us detect them, submit an abuse report via
http://www.report-abuse.dmoz.org/ including the details.
@4: That is a modified version of the main reason the ODP was created. Back then, all other directories failed to have their data current, because they simply lacked manpower.
I recently tried mining some other directories for links, and they were much worse than the ODP. Regardless of the efforts, a certain amount of rotten links can't be avoided, though. Sites go MIA all the time, and our voluntary editors time is limited.