Just like Christopher Nolan's previous movie The Dark Knight (2008), no second unit team was hired for making the movie. All the shots were filmed by Nolan himself with his usual DP Wally Pfister.
Just as Cillian Murphy's character was named Robert Fischer as a tribute to champion chess player Bobby Fischer, his father's (Pete Postlethwaite) character is named Maurice Fischer as an homage to artist M.C. Escher (full name Maurits Cornelis Escher), whose art was clearly an inspiration for many of the special effects in the film.
There is a series of numbers that keep appearing, on the front of the train the number is 3502, the taxi number is 2305 and the hotel room number is 5302.
Just after Cobb spins Mal's top and closes the safe door, the water in his cityscape is not moving or rippling. When he and Mal walk outside, the water in the background is stationary.
When Arthur arrives in the hotel to get Cobb for their ride on the roof, the reflection of the window reveals a moving boom pole, possibly a c-stand and the boom operator himself.
When Saito uses his teeth to pull the safety pin from a fragmentation grenade (extremely difficult in real life) the safety lever remains in place even after the grenade is thrown several feet into the opening of a vent.