The first reference occurs (at 22:30 in the video) when he is talking about Dedekind's XIth supplement to Dirichlet's Vorlesungen and says that a certain French graduate text on number fields is essentially based on that supplement.
Question Which book is he referring to ?
I think it is Pierre Samuel's Théorie algébrique des nombres, but would like to hear other people's opinions.
The second reference occurs (at 47:00 in the video) when he is discussing Artin's general reciprocity law and says that its formulation was so simple that apparently his contemporaries did not quite believe it.
Question Which arithmeticians does Serre have in mind ?
I believe he is thinking of Hasse in particular. Artin is reported to have said that Hasse told him that the conjectural general reciprocity law couldn't possibly be true.
Which other mathematicians of the time expressed their disbelief (before Artin actually proved his own conjecture) ?