When Tagomi is having his conversation with Juliana in the yard asking her for the Bikini Atoll film before returning to the alternate time-line, the cherry trees are blooming, indicating it is springtime. Previously, they watched President Kennedy's speech from the height of the Cuban Missile Crisis. The Cuban Missile Crisis occurred in October, 1962. The cherry trees would not have been blooming when President Kennedy made this speech.
When John Smith visits the surveillance center monitoring Juliana's apartment, an Ampex VPR-2 videotape recorder is visible in the lower corner. The American-made Ampex VPR-2 was introduced in 1978 in the real-world, and is inconsistent with other technologies seen in the series.