Let's make a start on this one.
A useful Dent date is 1876, which was the year in which they registered the famous triangle trademark in direct response to the number of forgeries circulating.
Next, it is possible to narrow a watch's date by the addresses it shows. Edward Dent moved to 61 Strand in 1843 and the firm continued to operate there until 1920. E Dent & Co occupied 4 Royal Exchange from 1886 to 1921. This particular combination leaves an unusually wide date gap of 1886-1921.
Finally we have movement #57573. You have to be aware, GJP, that dating from serial numbers is notoriously unreliable; firstly only very limited ledger data is available, and secondly the period between making a movement and casing it was variable in those days so dating from hallmarks is not reliable. Mercer's book on Dent suggests that this movement number dates sometime after 1906 and probably before 1920. However, that is a dating from the general run of movement numbers, but is contraindicated in Mercer's by three Badollet movements in the 57xxx range which date to 1861 (from ledger records)!!!
I once owned Dent #59447 whose (original) case dated to 1920 from hallmarks. If that watch was actually made in 1920, then I'd suggest yours was made before World War I in 1914.
Let's move on to the case. It's Sterling silver, the (unseen) hallmark is for London 1910 (for which it must be a lower case serifed "
p") and the casemaker is John Woodman of London (registered in 1897). You don't say if the case has the serial number 57573 to prove it is the original case, but assuming it is then I think the date of the watch can reasonably be assumed to be 1910.
Gosh, I bet you thought this was a precise process
And finally, the "military" bit ...
You're obviously referring to the "WD" mark on the dial. The first thing that is strikes me is that the exact style of the arrow is not quite right. It's slightly fancified, the flanges of the arrow are too tapered and most importantly the painting on the dial was not good quality - it has flaked, and that is definitely not Dent quality. That last fact demonstrates that this is an after-sale addition, and I suggest that it was done by the owner of the watch.
All of that actually supports the watch date of 1910. I would guess that the watch was owned by an army officer (or maybe cadet) who was posted to Europe in 1914 and decided to have this put on his watch to demonstrate its credentials as an "army watch". For an officer in the field a watch was essential equipment, and it wouldn't surprise me if officers had to buy or use their own, and perhaps having the WD logo was a requirement.
Incidentally, Dents in silver cases all seem to have been bought as "working watches" - the large majority of their pocket watches were cased in gold.
I note that you had some problem with posting your photos GJP, but I'd still very much like to see the case markings and the movement. Would you try again please?
it also has 1 0 2 above a G
Are we sure which of the Dent companies Audemars were supplying, Paul? Is there an address? Whatever, my guess is that Audemars were not marking their movements with their own numbers, but were leaving Dent to put Dent numbers on the movements. 
