Homer's last gifted idea, warmly received by Elon Musk, is "On the Miami Dolphins helmet, the little dolphin is also wearing a helmet." This was no longer true by the time this episode was produced (in 2014) or aired (in early 2015), as the team changed its logo before the 2013 to a swoosh-like design of a turquoise dolphin without other features. Homer would have been correct if he'd spoken about the dolphin-helmet design in the past tense, but he didn't.
Burns suggests they sing a song from "the last Depression." But the song performed is "Blues in the Night," which was written in 1941, long after the Great Depression had ended.
When Elon Musk looks out the window during their dinner the moon is pretty much exactly in its third quarter and well over the horizon. In the northern hemisphere such a moon is only visible roughly between midnight and noon, an unlikely time of the day for the Simpsons to have dinner.