Dylan used a variety of capos in the throughout the '60s, both the cloth and rubber Bill Russel Capo and the metal and plastic capos. The Kyser clamp on capo which most musicians keep on the head of their neck was not in use then. Dylan used the capo on both acoustic and electric guitar. A lot of guitarists won't use a capo on electric though a lot of blues musicians do. Keith Richards uses a capo on electric and has specific guitars with the capo on specific frets. I know this from a press kit from the Steel Wheels tour. Part of the reason for that is efficiency because capos will knock the guitar out of tune. The first time I saw Johnny Cash, he had two Martin D-45s with the capos on different frets. If he changed keys, he changed guitars.
If you check out the video from '65 (a Dont Look Back outtake) of Dylan doing, "It's Alright Ma," he has the capo way up the neck. He definitely used a capo on "John Wesley Harding," playing most of the songs in F, but playing in the C position, which is how he got the guitar sound for that album.
After the '60s, though I don't recall ever seeing him use a capo on stage, and never on the N.E.T.
For all you ever need to know about capos, check ths site out:
http://www.sternercapo.se/Capomuseum/
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quite funny. 