I agree that the term, cool, is inappropriate for a formal letter, research paper or even a magazine review if the audience is known to be experts themselves in the subject. To say a film is cool is reductive and might get a few of your readers rolling their eyes. Ironically, I believe that to be cool one ought to avoid using that expression; it's becoming overused, but that's my personal opinion.
The OP ought to consider how people from the 40s, 50s, 60s and possibly early 70s would have expressed the same concept. (Now someone will tell me that "cool" meaning impressive, admirable, inimitable, and wow was first used in 1800s or thereabouts.) 1
When I was living in London as a child, cool usually meant mildly cold or indifferent, wicked was associated with witches and criminals, and sick meant vomit. We did use bad though, when we meant "very good".
However, much depends on who your readers are. If I had to describe a new car or a hi-tech gadget, and compliment it on its design or features I might very well opt for "a cool design" and "cool features". But if I wanted to be more specific, (or original) I'd choose from one of these adjectives instead: (in no order of preference)
- sleek; streamlined; sexy; seductive; stylish; dynamic; innovative; astounding; impressive; breathtaking; elegant; smart; intelligent; unique etc.
For a film/movie review you would probably need a different list, unless you were commenting on the camera shots then many of those suggested above would fit. A "cool" movie could also be described as being:
- extremely popular; trendy; has a large following; modern; exciting; thrilling; exhilarating; inspiring; etc.
Actually, I'm beginning to realize just how versatile "cool" is...