I suspect Nick could see it because it was a visible to everyone. In reality, we don't have any videos of Hitler with those coins on his lapels. If Grimm takes place in our universe that means this isn't a video of a Nazi rally that anyone in the public has seen before.
This meshes nicely with the letter Kolt had from Himmler, as it was about how he had a responsibility to take actions to maintain the safety and image of the Führer. At first we figured it was just a stock letter sent to SS officers. But in light of the contents of the tape it could also be specific orders to keep the information on the tape from reaching anyone else.
Given the level of control Hitler had over the media, it's well within the realm of possibility for him to have confiscated or destroyed all other records of the event, and gotten everyone who might have seen it to never speak of it. (Even easier if he had coins with mystical leadership powers.)
(As an aside,
A film simply records whatever light/images are cast upon it... if it is a mystical thing, it shouldn't be recorded on the film.
The nature of something mystical is that it doesn't make sense. There's no rule that says mystical things can't also show up on film, except that in the real world, we don't have mystical things to record.
At least so far though, the show has had a relatively low level of mysticality (hereditary Grimm powers, poisons and weapons rather than spells, everything occupies normal physical spaces). So I think it's fair to ask the question in the first place, but "Because it's mystical" is an answer unto itself, not a reason it can't be.)