I also at first said to myself, "What dot?" But then had a closer look and there it was in some pictures.
Looking at catalog pictures and period (pun not intended) photos the dot seems to have gone out of favor in the late twenties. The catalog pictures are not entirely reliable and subject to artistic license, as the specifications for the 1927 OC shows both sides of the machine, one with and one without dot! Before this the use of the dot seems to occasionally be omitted, as a picture of the Douglas stand at the 1919 Olympia show has no dot on the marquee. But most photos before the late twenties show a dot.
The occasions where you see a dot on later machines, like post-war models, are instances where one can not rule out a restoration or replacement of the transfers incorrectly including the dot. I was not able to find a period photo of a post 1930 machine or company logo with dot in what literature I have excluding one example. That exception was in some publicity photos for the 1935 Endeavour [Briercliffe & Brockway, pg 68] showing a dot on one side and none on the other, but again these are clearly retouched photos. Likewise contemporary photos of veteran and vintage models without the dot, the instances where missing, look like machines that could have been restored and the dot incorrectly omitted. So sometime in the late twenties it looks like the dot went out of use.
The transfers have been available for Douglas machines for a long time, and no doubt over the years have been incorrectly made (and remade) with and without dot to further confuse matters for us folks today. For example the varnish affixing ones I got in the mid-eighties for my 1934 (white with black border) and Mark 3 (white with gold border) both have dots, though the evidence indicates this is incorrect. A snip with the scissors before application can quickly correct this!
-Doug