1: I created a custom scoreboard with this command:
/scoreboard objectives add a dummy Age

I displayed it with
/scoreboard objectives setdisplay sidebar a

2: I made a superfast clock with two commandblocks that fires 20 times in a second (see Screenshot 1)

Fill in the upper Commandblock:
/setblock ~ ~-1 ~ redstone_block

and in the lower one
/setblock ~ ~1 ~ stone

In the other Commandblock, fill in
/scoreboard players add @e a 1

Start the clock by placing the Redstoneblock between the Commandblocks. I recommend to run following command, so that your chat will not get spammed:
/gamerule commandBlockOutput false

3: Summon any Entity (I tested it with ArmorStands)

What I expected happening:
Mine and the Entity's score will count up without an end. When I am closing the map and load it again, nothing special should happen.

What instead happened:
As I reloaded, the scoreboard of the Entity starts from the beginning and a "Phantom" Custom Player is shown at the scoreboard. The score of the new "Phantom" Player is not counting up. My score is counting up without resetting as it should.

In Screenshot 2 you are seeing before reloading. Even when you can't see it in the picture, the score is actually counting up. Player "d42507a0-fd2d-4463-9b9a-c958fb5c3e92" is the ArmorStand. The Player "Rismosch" is me.

In Screenshot 3 I reloaded the world. The ArmorStand started from beginning and the new "Phantom" "d42507a0-fd2d-44" is not counting up. You have to use the following command to delete him:
/scoreboard players reset <Insert the Name of the Phantom Here>*

The Bug is, that when you reload the world, the game creates a Custom Player for each Non-Player Entity and it resets their scores

*(The Name of the "Phantom" depents on the summoned Entity. Because the Entityname is random, the "Phantom's" name will be random as well. Use the name that is shown in your game.)

PS: I used this Redstonemechanism first in 1.8.3. The Bug appeard suddenly in 1.8.4.