Doug Judy says the car is a 1961 Ferrari 250 GT California. However, the car shown is the 250 GT California Spyder LWB (long wheel base). This model was superseded by the SWB (short wheel base) version in 1960 already, easily recognized by its very different front design. There are no 1961 LWBs.
Rob Riggle's character is supposed to be a New York Firefighter, but he sports a full beard, which would not be allowed.
Off-duty notwithstanding, NYFD are strongly discouraged from visiting public bars wearing visible identifying marks of the NYFD, let alone from participating in drinking games.
Technically in order to win Shaw's back the Squad wouldn't need to drink a higher number of drinks, they would only need to drink more expensive drinks.
Jake says that all his grandparents are alive but previously stated that his Nana was deceased.