Update: 17:45 Thanks to Ryan for this little update.
A commenter says the "hooded woman" was Kate: Link
Also, made a longer video. Feel free to embed from YT:
Wow another interesting day of filming for the LOST crew and fans of Sawyer and Miles. Our good friend Ryan and several fans got to witness several scenes being filmed today and there is a good amount of detail to even perhaps confirm that Miles and Sawyer are partners in law enforcement similar to the Dharma Days in 1977.
Here are snippets right from Ryan's report of three scenes that were filmed:
One scene took place in front of a “La Brea Property Management” office in “Pacific Tower” (false signs hung on Kukui Plaza). Around the corner, two L.A.P.D. cruisers were parked. Sawyer is waiting in a new-ish but nondescript silver four-door Mercury sedan. Sawyer beckons to Miles, who cautiously walks up to the car, then tries to wave Sawyer off and walk away. But Sawyer calls out and stops him, leans over, and opens the passenger door for Miles.
Miles gets in. Sawyer gives Miles one of two cups of coffee, and they talk. Sawyer then gives Miles a file or folder with photographs, and he flips through it. He looks at one photo intensely, and hands it back.
Miles was wearing dark jeans, a blue plaid collared shirt, and a leather jacket. Sawyer was also in jeans, with a dark, rugged jacket over a gray T-shirt. Miles is definitely a cop, but this scene suggests that even Sawyer somehow again ends up involved with law enforcement. If he is working with Miles, it would appear the pair are a team, just like in the Dharma Initiative circa 1977.
Posters were hung, boxes were strewn, and a hose was used to add an extra layer of wet dinginess. A slight woman wearing a black jacket and with a grey hood pulled over her head repeatedly ran down the alley as a camera crew filmed her from above (perched atop the Thomas building). She knocked down a stack of boxes as she ran, which would then be carefully set back up for another take.
Car chase scene with woman who is being chased by the police crashes into Miles and Sawyer's Car. A nice video of the stunt is posted in Ryan's report at Hawaii Blog.
Summary of Filming and speculation of scenes from Ryan:
Though these scenes were obviously shot out of sequence, I’d guess it unfolds as follows: Sawyer flags down Miles from his car, and they meet, sipping coffee and looking over photos. Suddenly, a blue car involved in a police chase crashes into them. The driver, a hooded woman, takes off down an alley.
As I said these are just small snippets about the filming so check out the FULL and excellent report and video of stunt here: Hawaii Blog