Plenty to say, not sure how to say it.
For me, the visual style is 90% of what makes a notable director. All the ones that @Machine_Elf listed above (with the possible exception of Nora Ephron) have made films where as an audience member, five minutes of watching it would tell you who the director was if you’d gone in blind. I always thought the original four Alien films were fascinating in that it was the only franchise I could think of in which each instalment was helmed by a director with a distinct, recognizable visual style: Ridley Scott, James Cameron, David Fincher and Jean-Pierre Jeunet.
Then again, the cinematographer brings more than a little to bear on the final product as well. Oliver Stone is a director who I’d say had a specific look to his films, but how much of that was due to Robert Richardson’s lensing? He shot all of Stone’s films from Salvador through U-Turn, and the similarity in their visuals jumps off the screens. You can always spot a Richardson film, no matter the director: he’s shot things as diverse as most of Tarantino’s films, a lot of Scorsese’s since Casino, and even John Sayles’ City of Hope. Stone’s films have been less recognizable as such since they parted ways.
Editing was brought up as well. There’s a common saying in Hollywood: a film is written three times, once when it’s scripted, once when it’s directed, and once when it’s edited. Look at the editing in JFK, Natural Born Killers and Nixon and once again, Stone’s work has a trademark visual unity. He used the same kind of cross-cutting in U-Turn, in which is was wholly inappropriate, and that’s one reason the movie is one of his worst.
Spike Lee is a director I’ve long admired because he’s always remembered that film is a visual medium above all else. For a crash course in effective storytelling, watch He Got Game. I’ve been long convinced that one could watch that movie with the sound turned off (and maybe playing the Public Enemy soundtrack on loop in the background) and you’d still understand every single plot point, because the story is told so effectively through the cutting.
Back to cinematorgaphers, and speaking of Lee, his earlier films were all shot by Ernest Dickerson, and there’s a distinct similarity between everything from She’s Gotta Have It through at least Malcolm X. And yet…some of Lee’s specific stylistic quirks, like the dolly shots in which a character moves along the street while not seeming to walk, continued into later, non-Dickerson, films.So that’s on Lee and not his DP.
We haven’t even gotten into the more intangible things about a director’s work, like how they elicit performances. Some directors have a reuptation as “actor’s directors.” Some stars would cut their salaries to work with Robert Altman, because they knew it would be a great ensemble experience. Davids Lynch and Cronenberg are also able to get big stars for relatively cheap because those stars care about their craft and want to have interesting, challenging and talked-about projects in their filmogaphies. At TIFF one year, I saw Catherine Keener in a Q&A telling the audience that she’d accepted the role in Genova for no other reason than she wanted to work with Michael Winterbottom. I like a director who fosters loyalty among actors either through a good working environment, or by constantly offering them interesting work: Willem Dafoe will act in zillion-dollar superhero epics, but he’ll also star in Abel Ferrara’s latest, shot for pocket change in his own Manhattan loft. A mark of a successful director is when actors want to work with them.
It’s sometimes easy to see bad directing. Look at the original The Producers. Mel Brooks, comedy genius that he is, has no idea where to put the camera, the lighting is flat, and shots begin and end practically at random (the “Springtime for Hitler” scene is an exception). Then there are the journeyman directors, the ones I personally call “mechanics.” You see mechanics at work in the horror genre a lot: they and their team know how to construct a scene, editing it in a way that suspense is generated as if by flicking switches. They’re good technicians, but if you can tell the stylistic difference between Steve Miner and Rick Rosenthal, you’ve got a better eye than I.
Anyway…tl;dr, but to me (film school grad, but also that was in screenwriting and not directing), the signs of a good director are myriad and largely intangible.