0:39:43: Vincent then makes Max drive him to a jazz club called Daniel's,
described as being "in Leimert Park, off Crenshaw". 

And that's just where this exterior scene was shot:

After Vincent has shot Daniel, and Max staggers outside in shock, those exterior scenes
on the street (where Vincent throws Max on the cab and threatens him), as you can
see from the screencap above, were filmed right in front of the Cheerio's bar,
at 4333 Leimert Blvd. (between 43rd Street and 43rd Place), in Leimert Park.

But Cheerio's wasn't the exterior of Daniel's.  It was just next door and wound up in the scene.

As you can see in the screencap above, Max & Vincent actually exit from another building,
a small corner shop just to the north of Cheerio's, at 4331 Leimert Blvd.

But it is glimpsed for just three seconds, so if you blink, you might miss it.

That small building housed a real estate office back then. As part of the set dressing (to turn
it into Daniel's jazz club), they appear to have built a fake stone wall/sign at its north end,
and topped it with the neon name "Daniel's", and added the red awning.

Here's an enlarged freeze-frame if the moment:

Here is a Google StreetView of the fake club's location.

To the other (south) side of Cheerio's was a semi-legendary L.A. blues club
called Babe's & Ricky's Inn, at 4339 Leimert Blvd, which I suspect
was the inspiration for them filming on this block in the first place.

So much for the exterior.  But the interiors of Daniel's Jazz Club?

Those were filmed some nine miles away, inside the Grand Star Jazz Club,
at 943 Sun Mun Way, in L.A.'s Chinatown.

Here is a Google StreetView of Grand Star.

0:52:56: Vincent forces Max to take him along on a visit to see Max's mother in the hospital.

When we see Max and Vincent run out of the hospital, that is the
Long Beach Veterans Hospital, at 5901 East 7th Street, in Long Beach, CA.

In the screencap above, we are looking at the east side of the main tower (seen
on the left side), as well as a lower building in front of it (seen on the right side).

( The parking lot we see in front of the hospital is now gone -
replaced by a new, modern hospital building. )

There is no StreetView of this exact spot, so here is a Google Earth
aerial view of it, with a red arrow pointing at the door where they run out:

0:52:59: After showing that hospital exterior, the camera pans to the left, and shows us
a pedestrian bridge, that appears to be right next to the hospital.

It isn't.  They faked us out again.

That pedestrian bridge is real, but it's actually 20+ miles north of the Long Beach hospital, and
it spans the San Bernardino (10) Freeway in the City Terrace area (90063) of East L.A.

So, what is actually right next to the bridge (where they inserted the hospital shot) ?
Harrison Street Elementary School, at 3529 City Terrace Drive.

The southeast entrance to the bridge (where Max enters) is around 3481 Marengo Street.
And at the opposite (northwest) end, it winds up at 3546 Whiteside Street.

Vincent chases Max across the bridge and catches him, but not before Max
throws Vincent's briefcase down onto the freeway below, where it is run over
by a truck and crushed.  This comes into play later, because Vincent's
hit-list was in that briefcase... and he needs it back.

When they're running on the bridge (above), they're first running east up the entrance ramp,
and then they turn and run north/northeast across the actual bridge

Here is a Google StreetView of the bridge.