Going to migrate my own thread from JPLegacy since I put a lot of time and effort into it...
Grant's wristwatch has been previously identified as an Oris 450 cal, shown here:
And here is an actual screenshot of the watch, the best out there:
Take a look at the case lugs (the areas to the right and left of where the strap meets the watch) Notice the angles and almost faceted appearance of them.
The Oris doesn't have these and the sides of the lugs curve and blend into the curvature of the case:
Going by the best screenshot we have of the watch in the movie (above), I matched the watch to a 1945+ military issue "ORD" Department field watch.
The military had watches produced by most of the major US watch manufacturers during WWII, each fitting a certain set of standards, but they each had very minor differences. This case style with the more angular lugs came out in 1945 I believe, and was utilized up through the Vietnam war. It is known as the 1917-H case. Do a google search and tons of images come up.
There were 4 brands in particular that utilized this 1917-H case... Waltham, Hamilton, Bulova, and Elgin. The differences between these 4 are all VERY minimal:
First, lets take a look at some interesting points of the screenshot:
First, notice where the wording starts in relation to the number 11. This pretty much cancels out Elgin as Elgin's is a very narrow wording and starts relatively close to the 12.
Second, notice the gap between the hand pivot and the top of the sub-seconds dial. The only one to match this gap is the Waltham.
Last, notice that if you draw a line from the top of the 7 to the top of the 5, it goes OVER the hand pivot of the sub seconds dial. Once again, only Waltham matches here:
The only point I can see against the Waltham being the one is the fact that the screenshot we have doesn't appear to have two lines of text whereas the Waltham does. Well after analyzing frame by frame movie scenes I can tell you that the entire brand name disappears in most scenes at distance anyways so the likelihood that the distance and camera blur obscured and made the watch face appear to only have one line is completely possible. Heck, it's even hard to distinguish the detail on the hour hand in the good screenshot!.
I have found a few Walthams since initially starting this thread that only have one line of text, so as of now, this seems to be the most accurate version of the Grant watch: