The full name appears to be "mass line education," as part of the plan to train the people in communist doctrine. See Why China's 'mass line' movement is headed for a dead end by Chang Ping (South China Morning Post, 03.08.2018).
The required sense of “jag” here is this one, roughly synonymous with “trip”:
jag noun 2. a state of alcohol or drug intoxication
Tom Dalzell & Terry Victor, eds. (2006). The New Partridge Dictionary of Slang and Unconventional English volume II, p. 1084. Routledge.
So “lamp-post jag” refers to Teresa’s dream with the lamp posts in it, McCarty ...
One purpose for this characteristic might be to show that at the end of the story, Bascombe (despite his changed appearance) is essentially the same at the beginning of the story. Lafferty does this by showing that he still has this enormous appetite.
Or possibly, it's just to set up the last paragraph:
A Special Aspects Man is someone who looks into the cultures they find for special things in them. Witness that when he talks about the questions of what happens to their dead and their respect for their ancestors, it's thrown back into his lap.
As they observe, it's supposed to add something to their trip if they gain such knowledge -- but the ship ...
The Hobbyist by Fredric Brown
Brown's flash fiction short story "The Hobbyist" (1961) is about a man
named Sangstrom, who is in a desperate search for an undetectable
poison but winds up getting more than he bargained for.