There were different B-58's in the video. I believe that there were at least two different pods in the video.
The majority of them were of the MB-1C pod but some of the shots I believe were the TCP. Without seeing the underside I can't tell if it was the LA-1 Reconnaissance pod which was rarely used.
Most of the shots were of the MB-1C pod which had two fuel tanks and a W-39 thermonuclear weapon. The MB-1C was not commonly used and was discarded early on due to fuel leaks. One of the distinguishing characteristics of the MB-1C pod was that it had four fins. These four fins can be easily seen in some of the shots in the video.
The other option is that it was the The Two-Component Pod (TCP) being that it was the more common pod used on the B-58. The TCP was split into two separate components which may explain why it was called the two component pod. Sometimes the military does make sense. The lower part of the pod was for fuel and the upper portion was for the Mk. 53 nuke. The advantage of this is that the fuel subpod could be dumped independently of the nuke. The distinguishing characteristic of the TCP (besides the seam pattern) was that it had three fins. In some of the shots, I belive that the fin pattern (in the poor image quality) indicated a three fin pattern (120 degree) vice the four fin pattern (90) degree dispersion.
The B-58 was one awesome aircraft! Beautiful airframe and innovative technology.
And it just looked BAD.