My unfortunate total laymanship in terms of music surely endows me with sufficient (lack of) knowledge to reply.
This very lack, however, will obviously also make my answer too vague for my own satisfaction and surely any kind reader.
I cannot identify instruments, nor tell which kind of muting is being applied to a trumpet; I may not even be able to hear the difference.
Yet, I am able to pick some details, and appreciate it, but my inability to go beyond this mere perception makes it difficult to analyze such things and probably also recognize them in other scores.
Liner notes are very interesting to me when they explain such characteristics, up to a certain point; such things as intervals, progressions and whatnots are sadly lost to me.
I love Goldsmith's very idiosyncratic rhythm patterns, and from reading liner notes, I know some are 5/8 or 7/8 rhythms, but I don't remember which is which; I guess if I went back to the notes, listening carefully to the motives, I would be able to remember which is which, but I'm not sure I could identify this correctly in other scores by other composers, especially if it appears not in the percussion but elsewhere in the orchestration.
A similar example: though I am able to recognize a waltz (3/4) when I hear a "traditional" one, I may not pick it up if it's more subtle; for instance, I had not noticed Buck Roger's song/theme was a waltz, and only realized it when I read Stu Phillips' comment on Glen Larson's "country waltz"; then, it appeared shamefully obvious to me, but until then, the overal context had made me oblivious to it.
Besides knowledge, I need practice; I suppose I could improve my skills my spending some time studying carefully scores, by simply reading their liner notes, spotting this and that, comparing it to something that sounds similiar in another score, maybe even making a library of audio samples for reference, ...
Regarding instrumentation, I know I have been more aware of bass guitar since a bassist friend told me about it when speaking of film scores, nearly 15 years ago (gee, time flies); I thus realized and learned it's something that is particularly unobtrusive and seldom featured in the forefront, yet provides as important a background, a spine so to speak, as drum beats.
Regarding composers, I have noticed a few things, but I really lack the vocabulary. At some point, for instance, it struck me that John Williams often had a little "something", a sort of punctuation in the form of an answer from a "background" instrument, after musical phrases. Jurassic Park that may have been the score that made me aware of it-- as you see, it's very hard for me to explain.
The prime example I'm thinking of is "Welcome to Jurassic Park", starting at 4:59; phrases from the theme are played on violin, and little flute "flourishes" reply to each line, marking the overall rhythm of the piece; then, at 5:13, the instrument "families" are reversed, with a wind (clarinet?) carrying the melody and celli providing the punctuation with very short phrases that are totally different from the theme yet do not clash with it.
And then, sometimes, such melodic lines intertwine and exchange places, with the counterpoint prevailing-- now that I have Jurassic Park in my head, I have difficultoes finding an example, but I think it occurs in the "Gremlin Rag" or in the second movie's "Gremlin Credits"
All of this may sound terribly simple, obvious and commonplace to musicians, though.
Here are now two examples of paying attention to, and enjoying, the precise orchestration and not just the overall effect.
As stated in a thread on FSM's board, in which precisely I was inquiring about the exact names of the various instruments used (they are unspecified in the liner notes; I didn't get the list either, though I did get plenty of recommendations of similar scores), I love The Yakuza, and most particularly its opening track, from the very first note on; I love this "mystery" sound (which I first heard in '70's Columbo episodes)-- xylophones, "hanging tubes", triangles, whatever is used.
I also admire Goldsmith's expert layering of instruments, especially his rhythmic layers; I love it when he does this at the beginning of Total Recall: one beat, then another, then another layer; the paradigm certainly is Rambo III's "Preparations", where he spends a full two minutes (starting at 2:26) adding one percussion and rhythmic pattern over another (I don't remember how much I have been able to count-- 6 or 7) yet keeping it all perfectly clear; the instruments and rhythms don't clash but complement each other; then he ads more layers, of a more atmospheric kind. That's something I always enjoy, paying attention to the way it keeps building.
To summarize: my lack of musical skills makes me miss lots of things, but I do pay attention and note some details, and wish I knew more about music.