When Astrid brings her husband dinner and then checks his phone, her wedding ring jumps from her middle finger to her ring finger. Middle finger during the interaction with the husband and ring finger while working with the phone.
In the very last last scene where Rachel and Nick are celebrating their engagement with friends and family at the top of the Sands hotel, TA Curtis is briefly seen in the crowd as one of the party attendees. Given that he is supposed to be Rachel's colleague at NYU and the party occurred with little notice, his appearance is odd.
When the map of Singapore is shown and the indicator showing that Nick and Rachel's flight has arrived into Singapore, it stops at an area close to the nation's harbour in south Singapore rather than Changi Airport, which is on the extreme east of the island.
When the plane flight graphic displays the flight from New York to Singapore á la Indiana Jones, the line drawn goes over Europe. Planes would fly almost due north (358 degrees) to take the shortest route for this long (nearly 10,000 km) flight, i.e., over the North Pole and Russia.
When Nick asks Rachel to go to Singapore, he says "Singapore for Spring break". This would place the timing of the film between March and April of the calendar year. However, the Tan Hua (Queen of the Night Flower), which blooms on the second night after they arrive, only blooms between July and October.
When Nick is talking to his family about Rachel, he mentions that she teaches millennials. While Nick and Rachel's ages are never explicitly mentioned, we can guess by the 1995 flashback that Nick at least is of the age range generally accepted to be a millennial (early 1980s to mid-1990s). Nick and Rachel seem to be near the same age, making both of them millennials. Unless Rachel is only teaching graduate students, her students would be firmly placed in the Generation Z age range.