Although no dates are explicitly stated or shown regarding the action in the film, the license plate on the new car bought by Thunderbolt does have "1973" on it. Also, the sign outside the schoolhouse said it was only open June through August, so the film's story must happen in either June, July or August of 1973. The calendar on the wall of the Western Union office showed the 30th falling on a Saturday. In 1973, the only month where the 30th fell on a Saturday was June, so the film's story logically must be happening in June 1973. However, in an earlier scene at a diner, a folded newspaper near Thunderbolt shows an article headline that dates from November 1973.
After the crazy guy rolls the black Plymouth, you can see damage to the drivers side roof and the rear wheel on the driver side is bent at extreme angle. However, moments later when Thunderbolt and Lightfoot are going down the road neither signs of damage are apparent.
(at around 1h 0 mins) Mario stops by to see the boys, and gets out of his car in a pouring rain storm. The area behind him shows clear blue sky with bright sunshine. Seconds later, it's overcast; still later in the scene it's partly sunny; then overcast again.
The right front wheel air deflector falls off the Trans Am when Lightfoot drives it out of the wheat field and onto the gravel road with Thunderbolt hanging on the passenger door. It reappears on the car in the next scene driving on Sun Canyon Road and then again at the stop at Diversion Lake.
While the boys are working at jobs, the place where they stay has a calendar labeled 1972, but the movie White Lightning shown on a marquee was released in 1973, and the calendar on the wall in the telegraph office shows June 1973.
As Thunderbolt and Lightfoot are being chased by Red and Eddie, Lightfoot careens the stolen Buick Riviera off the highway and down a steep embankment. Clint Eastwood's character (Thunderbolt, in the passenger seat) has obviously been replaced with a dummy. In addition, in some of the shots you can clearly see a large camera assembly, mounted behind the back seating area of the Riviera.
When Red and Lightfoot are opening the wooden crates with crowbars, the lid on Red's crate opens completely with one pry and the Lightfoot even lifts the top on his crate up before he uses the crowbar.
Several items point towards the film being set in November of 1973. However, the late fall and early winter in Montana is beginning of very cold weather. The short sleeves worn by the cast, the presence of wheat in the fields and the fact that there are still trees with leaves indicates that the film actually occurs during the summer/early fall of that year.