There a multide of glitches/bug with the current generation of "Woodland Mansions" in the overworld.
Generation inside hills, cutting the hillside off and leaving a weird air-gap
When generating inside of terrain, one terrain block remains ontop of the center stone-fence of the mansion border (see pics)
Terrain blocks are also kept inside the chest rooms and in one other room (see MC-107558)
The lowest floor can also generate with holes, due to water & lava lakes being able to generate inside the mansion (maybe able to fix by updating the order in which certain world features are generated)
Non-Full terrain blocks (grass, etc.) are also able to cut through the base of the mansions. This also seems to be the case with some parts of trees (see pics)
How to reproduce:
Locate Mansion by using /locate Mansion
Look at the way the terrain interfaces with the mansion in Spectator Mode
Teleport to new part of world by using /spreadplayers ~ ~ 10000000 1000000 true @a
Repeat
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I confirm this. The mansion I located had a lake on the ground floor, leaves appearing through walls, and had cut straight through some houses of a nearby village.
This isn't quite a duplicate of MC-107558, although it does describe one of things mentioned here. This is more to do with the generation of the mansion in relation to the surrounding terrain.
This ticket originally included multiple different issues:
1. lakes cut out blocks without updating surrounding blocks
2. Trees generate through walls
3. Illager spawn location markers do not place air, resulting in single stone/dirt/... blocks in the mansion
4. Animals spawn on top of the mansion
5. this ticket
I've updated the summary and attached files to only include 5. Please update the description as well.
FYI, the details to find the mansion intersecting a village in the screenshot I added are below.
Seed: -6549889454106593879
Coords: -4917/83/-5993
This is also a good example of a number of the other issues relating to mansion generation.
@redstonehelper Whats with the holes in the ground cobblestone floor?
The support blocks don't need to support where there already are blocks (even flowers, yes).
Confirmed in 16w39c
Confirmed in 16w40a
Confirmed in 16w41a
Confirmed in 16w42a
Confirmed in 16w43a
Confirmed in 1.11-pre1
Confirmed in 1.11
Confirmed in 16w50a
Confirmed in 1.11.2
Confirmed for 1.13.1.
Confirmed for 1.13.2-pre2.
Confirmed in 18w49a. See 18w49a file.
Mansion generating inside of hills
Terrain Blocks spawning on top of stone fences
Both confirmed in 1.16.1 (see screenshot from 2020.07.16)
Can confirm in 20w51a.
Can confirm in 21w03a.
Can confirm in 21w05b.
Can confirm in 21w06a.
This report is about multiple issues, and I think you should keep it only about cutting through terrain.
For terrain that appears inside the mansion there is MC-140727 / MC-107594. For lakes generating inside mansions there is MC-107916.
The trees issue seems to have been fixed. Grass is still not replaced at the bottom, and if you remove it from here I could create a separate report for that.
For trees interrupting the foundation there is MC-129117.

Can confirm in 1.17.1.
Can confirm in 1.18.1.
Can confirm in 1.18.2.
[media]Version: 1.18.2
Seed: 5674588914129534515
Coordinates: /execute in minecraft:overworld run tp @s 2786 67 4464 95 20
In 22w15a
Can confirm in 1.19 and 22w24a.
Version: 1.19
Seed: 4373241205666815302
Coordinates: /execute in minecraft:overworld run tp @s 401165.96 84.00 8261.06 -92.39 17.97
Version: 22w24a
Seed: -1218851612612966176
Coordinates: /execute in minecraft:overworld run tp @s 108087.76 81.50 9774.80 -74.95 19.25
Can confirm in 1.19.2.
Version: 1.19.2
Seed: -5025199615634886011
Coordinates: /execute in minecraft:overworld run tp @s -662.70 76.74 388.09 -537.23 26.55
The image 2016-09-28_17.49.53.png appears to show an entirely different issue. Because of how the outer corner structure is layed out, it actually extends outward several blocks of air. The tree generated in this air-space, and the game assumed the leaves needed foundation blocks below them, like the rest of the mansion.
I can't say I ever ran into that issue though.
Point 2 of this report is actually covered by MC-203450; this report really should only be about 1 issue, rather than 5.
Not sure if suggestions are being taken on this issue. I've been tracking it since 2018. It looks like there are attempts to split this into multiple issues, but the solution would probably be a more holistic one that resolves all of them. Rather than fixing individual areas where the Woodland Mansion cuts the terrain, it looks like there needs to be a terrain buffer around the Woodland Mansion structure. This would be a zone around the structure with generation rules specific to the structure area, so that it can attempt to blend with the existing terrain. The Mansion itself is a pretty rigid structure. It doesn't blend well if it is just dropped into the middle of the forest. With a buffer area, there is an opportunity to create a more natural-looking entrance and keep the structure at a decent y-axis level, since it would have finer control over the terrain around the mansion than the default terrain generation.
Currently, the Woodland Mansion is one of the more neglected structures in Minecraft and doesn't really "fit" into the game's aesthetics given its harsh placement rules.
I know I'm placing this comment on a bug report. This may be better as a feature suggestion (like a Woodland Mansion rework). Let me know if there is a better place for this kind of comment.

Confirmed in 24w46a.
Can confirm blocks on stonefences and in the chestrooms for another DEFAULT map.
Blocks at the entrance seem to all be there