The Catalog of Copyright Entries (which is what you're pointing at) is pretty much the de facto source for renewal information between 1923 and 1978...ish. From 1978 on (published since 1950), you need to look at the Copyright Office website, which has an honest-to-goodness search engine for such things.
Depending on your particular needs, the next step is a visit to your local library for actual paper copies of the Catalog. Some renewals slip through without an original registration, so you'd usually want to check that, too, in cases where you're interested (or for types of works that Ockerbloom isn't following, like movies). Google Books does have some complete scans, though, so that's looking up.
After that, you're in the world of "the Copyright Office said it's OK," so that's (probably--I'm no lawyer or trained expert) defense if you're sued. However, the clerks at the Copyright Office aren't perfect, so some things slip through or aren't published properly. That's where either a trip to DC or hiring a lawyer comes in.
The goal there is to find the actual registration documents to make sure they match the Catalog and are actually valid. Of course, failure to find it might mean that it was merely misfiled, so even that's not foolproof, I hear, and why lawyers charge by the hour for the work--the more you pay, the further away from the obvious places they'll look.
Oh, and of course, anybody with contacts with the current likely copyright owner can probably ask them for their copy of the registration and renewal. If they don't see you as an antagonist or thief, I can't imagine why they wouldn't let you pay their lawyer to pull and photocopy the file.
I think that's everyplace.
OK, no, that's a lie, because it doesn't account for anything outside the United States. Plus, there are a handful of creators whose work was retroactively renewed (or copyrighted), usually because they're war heroes of one sort or another. But you'll see that on the Copyright Office website. I don't believe any of the works are relevant to us, though.
Oh, and in addition to the actual copyrights, the moderators here try to play it safe, because there's a chance that an unrenewed story might be based on a copyrighted work, which means that the original copyright owner has standing to sue. I believe the general line of thought is to use trademark as a guide, there: If the character is a "hot property," and was around before the comic in question, then it's worrisome. The Green Hornet is a pretty good example; unless someone can read the stories and say with absolute assurance that no material was taken from the radio show, there's a chance that the Striker estate (or whoever owns the character) can come a-knockin'.