You get these 4 boundary stones.

https://en.wikipedia.org/wiki/Boundary_markers_of_the_original_District_of_Columbia

The one in the east that normally is hidden of the diamond. Doesn't seem off by much but the + cross point.. it's close to this

https://en.wikipedia.org/wiki/Zero_Milestone

But it's kind of off. Then you got looking at the "N of the right point.. the left should be the same.. but there's 2 points over there.. so it's not off by much. That milestone is too much off compared to any leeway on the left.

Seems to intersect at this

https://en.wikipedia.org/wiki/Organization_of_American_States

But that wasn't there when they built the white house. It was this place in the + spot.

https://en.wikipedia.org/wiki/Van_Ness_Mansion

You also got this odd lock keeper's house across the street.

https://en.wikipedia.org/wiki/Lockkeeper%27s_House_(Washington,_D.C.)

Who knows.

Then there was this

The central white marble "compass stone" in the floor marks the center of the U.S. Capitol and is the point where the city is divided into quadrants (Northeast, Northwest, Southeast and Southwest).

https://www.aoc.gov/explore-capitol-campus/buildings-grounds/capitol-building/crypt

That's the capitol building though.. and it's not as close as these other areas to the + of the DC diamond.

That star on the floor though.. seems like it's kind of supposed to be like that area.

https://www.atlasobscura.com/places/district-of-columbia-center-point