You raise a very important and subtle question. The simple, and quite possibly incorrect, answer, is to run a checksum program on the DVD and compare the calculated checksum with the one published on the Knoppix web-site. However, ultimately, it is turtles all he way down.
There are three checksumming methods in general use for doing what you want:
The results of checksumming a Knoppix 8.1 ISO image are available on the various download mirrors where Knoppix itself is available - for example, http://mirror.switch.ch/ftp/mirror/knoppix/DVD/
How to checksum an ISO image and verify that it is legitimate is covered in the the Knoppix downloading FAQ here: Knoppix Downloading FAQ
However, note that you do not have an iso image, but an actual physical DVD, so you need to be aware of a couple of things.
1) You do not necessarily know that the Knoppix 8.1 on the DVD is meant to be exactly the same as the Knoppix 8.1 you can download. There could be minor differences which change the checksum. On the other hand, if the DVD and the ISO contain exactly the same data, the checksum will be the same - so if the checksums do match, you can use the procedure in the FAQ.
2) The layout of data on the DVD can be (an often is) different to the layout of an ISO image file on a disk. Essentially, one or the other can be padded with zeros so that the data fits exactly into an integer multiple of the minimum block size of the device the data is stored on. If the checksum program reads all the storage blocks including the zero padding, then if the block-sizes are different, you will get checksums that do not match. You are not the first to come across this issue, and solutions are outlined here, as you yourself found: Calculate md5sum of a CD/DVD
Verifying the checksum using md5, sha1 and sha256 and verifying the PGP signature are probably 'good enough' for your purposes. However, if you are the subject of interest of people who can influence your Internet connectivity and physical post, it is difficult to ensure the information you obtain through those methods is untampered with, which is why I made my 'turtles all the way down' comment.
Clive Robinson's comments about using software from magazine covers (assuming the magazine is bought from a random vendor) ensure that it is less likely that you will receive software that is specifically tailored for you. It does not protect against generic tampering.
Note that the checksumming programs, and PGP signature verification programs you use should also be trusted by you, so you would need to think about where you source those from, and indeed, the status of the computer you execute the programs on. The precautions you take will depend upon your level of (justified or not) paranoia. If you are an average law-abiding citizen, then downloading a couple of well known 'Live CD' or 'Live USB' Linux or BSD distributions and using the checksumming and PGP programs included with them is probably 'good enough'.