If you look on the tsdr search page at tsdr.uspto.gov you'll see that they offer four types of searches, by registration number, serial number, reference number or international registration number. A trademark's registration number is analogous to a patent's patent number. Knowing a trademark's registration number should be all you need to know to retrieve that trademark's registration certificate (ignoring for now the problems mentioned earlier that not all of them are online or were ever scanned). The serial number search gets interesting but then there's an unexpected turn! In 2010 I asked the uspto about searching by serial number and their reply is below.
What confused me was that I thought I could enter the serial number shown in a patent gazette (from a published and at that time yet unregistered trademark or from the copies of them shown in Mr. Wendel's book) in the serial number search box and be rewarded with its registration certificate if the trademark was eventually issued. What I did not know until the uspto explained it to me was that those serial numbers reset from time to time for the various reasons they explain below. In other words, the serial numbers shown in the patent gazettes are not unique. That's where the series codes come in! The series code precedes the serial number shown in the patent gazettes to make them unique. That's what the serial number box on the tsdr search page is looking for! Sounds simple right? It should have made finding the registration certificates for the applications shown in Mr. Wendel's book easy. The published dates are shown in the book so a simple look up of the series code should be all that's needed. The series codes should be multiplied by a million and then added to the serial number in the patent gazette. Example: if the patent gazette serial number is 1 and it was issued during series code 71's reign its unique super serial number (for lack of an existing term that I am aware of other then the ambiguous "serial number") is 71 x 1,000,000 + 1 = 71,000,001. Enter that number in the serial number box on the tsdr search page and you'd think good things would happen.
But here is where the twist mentioned above comes in. The super serial numbers only work for, you probably guessed it, live or recently live trademarks ("recently live" is another freshly coined term to indicate a trademark was alive in 1984 but is now dead. Trademarks began in 1870 so by comparison 1984 is recent). Nearly all the trademarks in the book or of interested to Historic Intellectual Property fans are most likely long dead so their super serial numbers do not work in the tsdr's serial number search box. I analyzed the super serial numbers in tsdr and found thousands, in fact hundreds of thousands of cases where the super serial number = 60 Million + the registration number. That's an undocumented series code of 60! Many times all I have is the patent gazette serial number, like the ones shown in the book, and it's the registration number I'm looking for! I wouldn't know the super serial number to enter since all I have is the bleepin' patent gazette serial number! They might as well take away serial number searches on the tsdr search screen as it will only annoy Historic Intellectual Property fans.
There is an interesting distinction between patents and trademarks. Patents expire while trademarks can be renewed indefinitely as long as they are continuously used in commerce (and the owner pays each decade to renew them!) The oldest trademark still active by renewals, issued July 4, 1884, is Samson for rope so there is nothing inherently wrong with a Historic Intellectual Property enthusiast being interested in live trademarks! I hedged above by saying "most likely long dead". The Samson trademark turns out to be a good example of two other aspects of tsdr, one good and one not so good. The good one is that there are all sorts of interesting documents available online for this trademark! There are copies of legal documents going back and forth between the uspto and the trademark holder and images of packaging etc. Select US Registration No. from the dropdown, enter 11210 in the search box and click on the documents tab. Alternatively a serial number search for 70011210 works. A bad thing is documentation like this is generally only available for live trademarks! For a whole lot of dead trademarks all you get is a registration certificate if it's online and was scanned.
Another distinction between patents and trademarks, while not exactly relevant here, is that the trademarked item had to exist- unlike a patent which could be issued but may never had been produced. You couldn't trademark something for the fun of it. It had to be used in commerce.
Even more on super serial numbers and series codes.