Pam is making a Kringle and says it's the Wisconsin state pastry; that didn't happen until the year 2013. However, this is a dream sequence of comatose Archer, and dreams often are not factually accurate.
The dog fight between Archer's Polikarpov I-15 and the Messerschmitt Bf 109 is completely wrong. While the Bf would have been able to fly about 100 kt faster, climb, dive and accelerate faster, it would not have been able to turn as tightly as the biplane, and risk stalling when slowing down to the biplane's top speed. The German pilot would, therefore, not have been able to stay behind the Polikarpov all the time and fire at it but rather would have to swoop down at much higher speed, fire a burst, overtake it and fly a large turn or loop to get back into a firing position. However, this is a dream sequence of comatose Archer, and dreams often are not factually accurate.