Corrected entry: Falcone meets Fish's mole for the first time and describes the aria she is singing. It's name is Vide Cor Meum. The song was produced by Patrick Cassidy and Hans Zimmer for the movie Hannibal (2001). Therefore as Gotham is set sometime in the 90's-2000's and given Falcon's age it would be impossible for him to have grown up listening to his mother singing it to him. (00:15:00)
Corrected entry: When Bruce erects his pile of stones in the forest for his parents, one has the initials TW for Thomas Wayne, but instead of the other bearing the initials MW for Martha Wayne, it shows BW, as in Bruce Wayne. (00:23:30)
Correction: The pile of stones were not for his parents, nor was it a pile made that day. The hike was a tradition of Thomas and Bruce and during their hike they would collect a rock to add to their pile. So it's Bruce's pile and Thomas' pile. The size of the pile indicated how many times they went on the hike together. The scene is meant to convey Bruce's loneliness and loss. This is why Alfred does not go with Bruce (because it was only a hike he and his father took) and this is why after Bruce picked up the first stone, he pauses before picking up a second stone. The first stone was for his pile and he latter decides to pick up one for his father. Bruce's anger over the loss of his father is seen in his tantrum when he starts to throw the stones from the piles.
Correction: Gotham isn't set in any specific timeframe - the creators have deliberately said that the time period is vague.