I believe that from the timestamps the smear happened in the LM between EVA 1&2, like Willoughby. Note the image 114-18443. If you zoom up on the image you will see streaks in the direction of film rotation. This image and the next are "unusable" except they may have been taken inside the LM. And as Jet indicated in his video the magazines were changed in the vacuum of the Moon.
Ok, I no longer believe the contamination happened in the LM. I had some figures wrong, and then I was wrong some more. Here is a crude time line for the three magazines shot in the camera :
MAG 114 was put into the camera. This was the only roll in the camera during EVA 1, and the last photo taken was AS16-114-18443 at the end of EVA 1.
The crew then spent some time in the LM between EVAs. At this point, MAG 107 was put on this camera - starting with AS16-107-17495 at station 2 of EVA 2, and ending at AS16-107-17583 at station 9 of EVA 2 (the whole magazine). Then MAG 114 is put back into the camera, and the next shot is AS16-114-18444 (the beginning of the smudge), and this shot is taken at station 10 of EVA 2. So, this magazine is not put onto the camera until they are at station 9 or 10 of EVA 2, and there are plenty of photographs taken on EVA 2 on MAG 107 that do not contain the smudge. This makes it pretty apparent that the plate got compromised while switching between 107 and back to 114 to finish out the magazine.
AS16-107-17583 was taken at GET 06:04:24:25 (photo does not have smudge - taken at station 9 of EVA #2)
AS16-114-18444 was taken at GET 06:05:18:00 (very next photo taken with this camera - has a smudge - taken at station 10 of EVA #2)
Now, I'm not entirely familiar with the system. Is the plate part of the magazine or the camera? If it is part of the magazine, then the contamination could still have occurred in the LM between the two EVAs when they cleaned them. If the plate is part of the camera, then the contamination necessarily occurred sometime between 06:04:24 and 06:05:18 when switching from MAG 107 to 114 - this was during EVA #2, so obviously not inside the LM between EVAs.
One thing that can be cleared up is I think AS16-114-18443 is irrelevant because the entire MAG 107 was shot between 114-18443 and 114-18444, none of which contain the smudge.
EDIT :
The remainder of MAG 114 is shot during EVA #2 and all shots after AS16-114-18444 contain the smudge.
Then for EVA #3, MAG 116 was put into the camera, and every shot has a smudge.
And I have basically just restated what Astrobrant says in his original post.