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Thanks for your responses.

I would like to find out whether the use of SEOMOZ rank tracker violate Google's guidelines.

"Don't use unauthorized computer programs to submit pages, check rankings, etc. Such programs consume computing resources and violate our Terms of Service. Google does not recommend the use of products such as WebPosition Gold that send automatic or programmatic queries to Google."

Great feedback!  I still just have 1 remaining question, though, which I've posted below Richard's comments.  Thanks!

The trademark issue is with the names of the subfolders, not the domain name.

Thanks for that tool!  I was not familiar with it.

This almost fully answers my question.  Those pages don't have inbound links from other sites.  We have over 10,000 pages on the site, so we can't have links to them all.  So, they aren't worth keeping for traffic or links.

But you say, "I would hope that you capture your 404 errors and 301 redirect all the time anyway."  So, my last remaining question is: Am I necessarily creating 404 errors by not redirecting?

Thanks, everyone!

Yes, these are just pages on our main site.  They will be renamed, and we will be keeping the content on the site.

Thanks for this reply, and for the others!

OK, so the fact that your site has broken URLs doesn't bring your site in general down in the search engine rankings?  Broken URLs aren't necessarily an indicator of a poor quality site that would result in some sort of penalty?

We are using some branded terms in URLs that we have been recently told we need to stop using.  If the pages in question get little traffic, so we're not concerned about losing traffic from broken URLs, should we still do 301 redirects for those pages after they are renamed?

In other words, are there other serious considerations besides any loss in traffic from direct clicks on those broken URLs that need to be considered?

This comes up because we don't have anyone in-house that can do the redirects, so we need to pay our outside web development company.  Is it worth it?