The bug:

On a singleplayer world, when you ride an entity (minecart, boat, pig, horse, ...) and quit the world, the entity will lose all of its scores.

What I expected:

The entities should keep their scores.

How to reproduce:

1. Create a scoreboard objective: /scoreboard objectives add boat dummy
2. Set the score to display on the sidebar: /scoreboard objectives setdisplay sidebar boat
3. Obtain a boat, place it down, enter the boat.
4. Set a score for the boat: /scoreboard players set @e[type=boat,sort=nearest,limit=1] boat 1
5. Exit the world.
6. Enter the world again.
7. Notice the boat's score disappeared from the sidebar.

Notes:
Entities riding other entities don't seem to be losing their scores.
Did not test the behavior in multiplayer.