You can take the pursuit of details too far, I believe. A lot of screenwriting teachers feel that you should know much more about your characters than your audience will. You should write full backstories for all your characters: where they went to school, what they majored in, what mom did for a living, what they ate for breakfast, etc. ("Backstory" is movie jargon for stuff that happened before the events on screen.) The theory is that this will help you give your characters life.
It may - to you, anyway. The danger is that your audience can only see what is actually on the screen. The reader can only learn what is on the page. If something's not in the screenplay, how do we know it? Can the knowledge somehow trickle down into the character you're writing?
How will you know if it doesn't? You've got a wonderful deep, rich, rounded character in your head. You're writing wonderfully understated dialogue, given subtle shadings by the character's unique personality.
Unfortunately what may really be happening is that you are writing characters whose deep, rich inner lives are a secret known only to you. The dialogue just sits there, and nothing will lead us to suspect the character has any inner life. Your character's offscreen life or background has no reason to exist except to the extent that it affects the character's presence onscreen.
Personally, I like to discover things about my characters as I write what they say and do. I let them say things, and then I say to myself, "Wow, I didn't know that about Gail, that's great, I can use that!" This means I can also give my characters backstory that is convenient to the screenplay at the drop of a hat; and it means that anything I know about the character is in the screenplay.
To give a sense of a minor character, you can often show just a hint of offscreen life. Give us a hint of what they were doing just before the scene started. If your cop is going to talk to a shop owner, you might start the scene with the shop owner trying to charm a pretty customer, or shouting at some rotten kids, or haggling with a supplier over the phone. That gives us a glimpse into his life, and also gives him an attitude coming into the scene.
Roger Zelazny, a marvelous science fiction and fantasy writer, has an interesting technique. He writes a scene with his character that he does not put in the story. Not a whole backstory, just a scene. He then refers to the scene in the story. That gives the audience the feeling that the character has a life of his own. On his website, screenwriter Terry Rossio (The Mask of Zorro) discusses the same idea, quoting the original Star Wars Obi-Wan Kenobi tells Luke that Darth Vader "fought with your father in the Clone Wars," although we didn't learn what the Clone Wars were for another quarter century.
But note how this is different from a whole backstory. What makes this technique effective is the moment in the screenplay or movie where someone refers to the scene. Don't overdo it, but it may be worthwhile for your characters to refer to events outside the story. You don't have to pay off every setup.
There are characters you may not want to flesh out much. A good stock character can be great fun for the audience. The obnoxious store clerk. The befuddled grandfather. Do we really want to know their angst? No, they wouldn't be as enjoyable.
And then there are villains. Take Alan Rickman's over-the-top Sheriff of Nottingham in Robin Hood, Prince of Thieves. Did we want to know what made him the way he is? We did not. We wanted him pure, unadulterated evil. Any explanation would have made him less fun. What makes cartoon villains and stock characters good is the sheer verve with which they're portrayed. We love to hate the Wicked Witch of the West, or any of the James Bond villains (Dr. No, Goldfinger, Dr. Ernst Blofeld, etc.). They revel in their own evil, and we get a kick out of it. The stronger an impression your villain makes, the greater the obstacle for the hero, the better the conflict, the more drama.