Andy is correct there is no ranking plus/minus by the fact Google using the DMOZ title, but it can mean that the title you have is not effective in terms of CTR, or at least Google's system is thinking it can do better CTR with DMOZ.
Now since CTR like Andy says does play into the algorythm at Google having the title changed to something else can effect the CTR which an effect the traffic which might be what you are seeing.
Best to take control back of the site with the NOODP tag, here is the official information from Google on the tag and DMOZ use: [google.com...]
I've had the same thing happen to one of my sites. When searching for the exact site name, it still shows the ODP title (with sitelinks).
It used to show the ODP title for all searches, but now it shows the correct site title when searching for more generic terms. This makes me think that it could be related to site authority, because as the number of links and traffic to the site increased, the ODP data was used less often.
for *example* my "title" in DMOZ and now Google is John Widgetland whereas my Meta title is Guide to Growing Widget.
It's likely that Google is switching to your ODP title because they don't see your title as sufficiently relevant to whatever search query brings it up.
Gogole has changed my listing title and now using my DMOZ listing title not my Meta title. Which very likely has caused a major drop in my listing rank.
I'd see the DMOZ title more as indication that your title might be enhanced... not as a cause of ranking drop. It's a display isssue only.
While adding the NOODP tag will restore the display of your page title element to the serps page, it may be that you can help your overall rankings by adjusting your title... perhaps, in this case, a longer title that includes "John Widgetland" at the end.
On the other hand, "John Widgetland" might not be all that competitive and you may have that search locked up, so the NOODP tag would suffice.
I think it's prudent to include the site name in at least the home page title, though not necessarily at the beginning.