Robert Capa uses a Leica camera with a Summar 5cm lens. This type of lens needs to be extended out from the camera to enable it to focus an image onto the camera's film. However, in the movie, the Leica's lens is shown in its collapsed, unusable position, even when Capa is taking pictures with it.
Actors are seen smoking filtered cigarettes. These didn't become widely available until the 1960s.
While Hemingway is looking for Nazis around Cuban waters he is seen wearing a camo shirt with cut off sleeves. That pattern is Woodland Camouflage and it wasn't available until 1981.
In one of the Spain scenes, Gellhorn shows up in a T-34/85. The scene takes place in 1936. No T-34s of any type appeared in Spain. The T-34 in general did not appear until 1940. The T-34/85 came into service in 1943. The tank in the movie was probably meant to represent a T-26, which are harder for filmmakers to find.
During the scene at the hotel, after the bomb (51'23"), Hemingway is shown using a photographer's vest with a plastic zipper. These weren't made until the 60's.
During the Spanish civil war you see a Citroen Traction Avant 11B with a big booth. This model was first made in 1952, 15 years later.