One of the key factors is that titles are re-written in a way that depends on the query. For example, if the search phrase is the domain name, then the algorithm often ADDS the domain name to the title if it isn't already there.

You can use the meta tag <META NAME="ROBOTS" CONTENT="NOODP"> to request that Google not use the DMOZ title. However, using the out-of-date title from a 301 URL is something new to me. Sounds like a case of Google taking the 301 status quite literally: "the requested content has moved permanently to a new location."

Thanks, Ted.

I have a screenshot that shows the problem. Ted took it out because it is a domain search. I can share it privately with anyone who wants to see it; just message me directly.

Having edited at DMOZ for years, I would highly suggest to Google that the titles written by DMOZ editors not be used in search results.

The reason is that the titles are meant to be used only in the context of the page on DMOZ. That page is a clearly defined category. The DMOZ guidelines state that the web pages listed in that category should NOT use the name of the category in the title or description. Otherwise each page on DMOZ would be filled with very repetitive listings.

So on the "Widgets" category page they want to avoid:
Bob's Widgets - Seller of industrial widgets for commercial use.
Widgets by Jane - Creates widgets for home widget use.
Widgets - A site for widgets.

Instead they want:
Bob's - industrial quality seller for commercial use.
By Jane - Created for home use.
Emporium - Large selection for all types of applications.

Google's handling of redirection is quite odd.

There was a page with a particular word on it and that page appeared in Google SERPs when that word was searched for. Two years ago, that page was deleted, and a redirect installed pointing to another page, a page that has been online for far longer. Although this other page is on a similar topic, it does not include that word nor any synonym of it. The redirected-to page appeared in the original SERP as soon as the old page was deleted and the redirect installed. At first I thought this would be temporary, just some effect of the recent redirect. Two years later, that page still ranks for that word, even though that word has NEVER been on that page. That word appeared only on a page that no longer exists, the URL of which has returned a redirect for the last two years.

There sure is a bug in the attribution of content to a URL. The logic is very fuzzy. It's also tied in with canonical handling in some way.

any chance that could be affected by anchor text referring to the deprecated url?

No. Not at all. Not anchor text.

It's as if the entire body content of the old (now deleted) page is attributed to the URL the missing page is now redirected to.

yes, I am noticing this since march 2011 and this seems to be a deliberate change done along with the major update.

When the "old content" can stick to a redirected-to page, it can very well do with an existing page and think of folks doing major content changes to address the update, yet not finding any improvements!