The movie is set in 1968, but The Sapphires sing The Staple Singers' "I'll Take You There" (released in 1972) and Merle Haggard's "Today I Started Loving You Again" (released in 1970). It also features "Run Through the Jungle" (released in 1970) in the opening scene.
Throughout the movie the girls are seen performing on Shure SM58 Microphones which were released in 1966. This is chronologically correct as the movie is set in 1968. However when they are performing to the 19th Infantry Division in Nha Trang, the microphones being used are Shure Beta 58 Mic's which weren't released until 1989.
The "blackened catfish" is both an anachronism and a factual error. "Blackening" is not a traditional Cajun cooking technique. It was invented by Chef Paul Prudhomme in the late 70s and popularized by him in the 1980s.
No US Soldier "in country" would have been in possession of US currency - only "scrip" (a form of pseudo money) was used. Scrip could be exchanged for US money only on leaving the country. Possession of US currency was an offense subject to court martial.
The US army give them a 1940's Citroen car with the driver seat on the right side which could be found in Australia but not in Vietnam. France's colonial Indochina, actual Vietnam or the US drive on the right and have the driver seat on the left.
When Dave and the Sapphires first arrive in Vietnam, they are being transported in two M151 Mutts. The Mutts simply have "US Army" stenciled on either side of the hood. There are no registration numbers and when viewed from behind, both vehicles have also civilian license plates.
The goof item below may give away important plot points.
When the girls go to visit Dave Lovelace in hospital, a modern wheelchair with "Economy" back wheels is pushed across frame in the background. Standard spoked "bicyle" wheels were the only option until the 1980s.