
0:04:05: We see Max putting gas in his taxi at a "Gas & Market" featuring a large
mural of Our Lady of Guadeloupe (surrounded by produce). It is next to a freeway.

This is an actual truck stop. You'll find it at 1400 South Alameda Street,
on the southeast side of downtown Los Angeles, an industrial
area dominated by warehouses and factories.
The freeway seen behind it is the Santa Monica (10) Freeway.
( In the screencap above, the camera is looking southwest. )
But the place has changed quite a bit. The mural was never really part of the
station (it was copied for the movie from a shop in East L.A.) And instead of
the sign reading "Gas & Market", it now reads "Diesel & Propane".
Here is a matching Google StreetView.

0:04:53: We see Max stop and pick up 'Annie Farrell' (Jada Pinkett
Smith),
the female prosecutor whom he later rescues.

This pick-up scene was shot outside the Airport Courthouse, at
11701 S. La Cienega Boulevard, just a little southeast of LAX,
at the interchange of the 405 and 105 freeways.
In the screencap above, the camera is looking west, as the taxi
pulls out the courthouse lot, onto La Cienega.
( The view looks somewhat different today, because they later
built a large apartment complex right next to the courthouse. )
In the screencap below, the camera is looking north/northwest
up La Cienega, towards the 105 Freeway overpass.
Here is a matching Google StreetView.

0:09:32: After Max picks up Annie (and they talk in the cab) he supposedly drops
her off at 312 Spring Street, in downtown
Los Angeles. That is the actual
address of the old Federal Courthouse in Los Angeles,
near City Hall.
(You can see the actual Federal Courthouse here.)
However, in the film, Max is actually seen dropping her off at
the
northeast corner of 5th Street & Grand Ave, in downtown L.A.
about 1/2 mile to the SW of the courthouse.
In the shot above, his taxi is headed west on 5th Street, just east of Grand Avenue.
(You can see part of the central Library on the left.)
Here is a matching Google StreetView of that corner.
That is the location of the Gas Company Tower, which,
at 52 stories, is the 4th tallest skyscraper in Los Angeles.
In the movie, the trip takes about seven minutes. In real life, the trip from the
Airport Courthouse to 5th & Grand is 15 miles, and would take 23 minutes in good traffic.
( Unless he followed her instructions to "take Sepulveda to Slauson to La Brea to 6th" -
rather than just take the freeways, which would actually stretch the distance to
19 miles, and might double the time to needed to drive there. )
0:13:50: And when we see 'Vincent' coming down the escalator in an office building
(as he passes Annie going up), that is precisely where he is: inside the
Gas Company Tower, at 555 W. 5th Street (at Grand), in downtown L.A.
(Remember this location, it shows up again later.)
0:13:55: That same corner (of 5th & Grand) is also
where Max first picks up Vincent, as a fare (seen below):