The bug
When a zombie starts breaking a door and during this the door gets replaced the zombie continues breaking this block.
Additional description by @unknown:
If a zombie begins to break a door but the door is removed before it's done, it will continue to try to break the block in that space. The door breaking sounds will continue to play even if there isn't a block there anymore, and the door particles will appear when the door would have broken. If the door is replaced with another block, that block will be broken instead, no matter what it is.
Expected behavior
Zombies and vindicators should not continue to break doors once a change in blocks has been made.
Reproduction steps
Ensure that the difficulty is set to "hard" and the "mobGriefing" gamerule is set to "true".
/difficulty hard /gamerule mobGriefing true
Build the setup as shown in the attachment below:
Whilst standing on top of the diamond block, summon a zombie that is able to break down doors.
/summon minecraft:zombie ~ ~ ~ {CanBreakDoors:1b}
Stand on the opposite side of the door as the zombie, switch into Survival mode, and get it to notice you.
Once it begins breaking the door, switch into Creative mode, destroy the door, and watch the behavior of the zombie closely.
❌ The zombie continues 'breaking' the non-existent door
How to reproduce (outdated)
Additionally:
Set the difficulty to "hard"
Spawn the zombie or vindicator with
{CanBreakDoors:1b}
Note: The meta data of the placed block should not have bit 2 (22) set, otherwise the zombie will recognize it as open door.
Related issues
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Can confirm.

Confirmed in 1.9.1-pre3. Relates to MC-1.
To clarify the issue a bit, if a zombie begins to break a door but the door is removed before it's done, it will continue to try to break the block in that space. The door breaking sounds will continue to play even if there isn't a block there anymore, and the door particles will appear when the door would have broken. If the door is replaced with another block, that block will be broken instead, no matter what it is.

I also encountered this bug when multiple Zombies break a door, after the door breaks, the other Zombies who started breaking the door not initially will break the air blocks.

16w42a: Replacing the door by hand no longer exhibits this behavior, but /setblock and related methods of placing blocks (note that this can be accomplished in survival using, for example, an end portal) are still affected.
Cannot reproduce in 1.11.2 by using /setblock nor by replacing the block manually. (Fixed?)

Still reproducible by /setblocking the top block of the door to some other block when the zombie is close to breaking it.

This issue relates to the first ever bug report on this website! How awesome 😃

Confirmed in 1.16.1.
Can confirm in 20w51a. Make sure your difficulty is set to hard
and to make it easier use the {CanBreakDoors:1b} tag.
Can confirm in 21w05a.
Can confirm in 21w05b.
Can confirm in 21w06a. Video attached.
Can confirm in 21w17a.
Can confirm in 1.17.
Can confirm in 1.17.1.
Can confirm this behavior in 21w40a. Here are some extra details regarding this problem.
The Bug:
Zombies and vindicators will continue to break doors despite a change in blocks.
Steps to Reproduce:
Ensure that the difficulty is set to "hard" and the "mobGriefing" gamerule is set to "true".
/difficulty hard
/gamerule mobGriefing true
Build the setup as shown in the attachment below.
Whilst standing on top of the diamond block, summon a zombie that is able to break down doors.
/summon minecraft:zombie ~ ~ ~ {CanBreakDoors:1b}
Stand on the opposite side of the door as the zombie, switch into survival mode, and get it to notice you.
Once it begins breaking the door, switch into creative mode, destroy the door, and watch the behavior of the zombie closely.
Observed Behavior:
Zombies and vindicators will continue to break doors despite a change in blocks.
Expected Behavior:
Zombies and vindicators would not continue to break doors once a change in blocks has been made.

Please don't fix zombies can break bedrock
Can confirm in 1.18.1.
Can confirm in 1.18.2 and 22w11a.
Can confirm in 1.19.
Can confirm in 1.19.2.