Indeed, the ending of “I Can’t Get Started” does sound somewhat cartoonish.
I like the topical references in the lyrics—to the Spanish Civil War, FDR, and Hollywood movies—appropriate for a song from the early months of 1938.
Not being a musical expert, I wasn't sure if my perception was off base about the ending eight notes or so. If I were in charge (perish the thought!), I think Bunny Berigan's few notes of that superb trumpet solo would have been a nice ending, in tune with the overall mood of the song.
Yes indeed, the lyrics are quite the period piece from that era: Garbo, Metro Goldwyn, charting the North Pole and flying around the world in a plane. Still, the song holds up really well nearly 80 years later.