I was messing around with old worlds when I found two things:

• Redstone would not power, despite being directly connected to a redstone torch. 
• Using spawn eggs, various mobs could be spawned beyond the world border with little effort.

The first bug had me totally stumped and is very easy to set up. Simply place some redstone next to a redstone torch and witness literally nothing happen. I tried this in two worlds and it's consistent. 

The second bug seems to make more sense to me and is also very easy to do. In Creative mode, get a spawn egg and spawn mobs near the border. If you're lucky and get the angle just right, the mob will be dark and frozen outside the world. Hitting it will make it keep the red shade forever and effectively make it invincible. Interestingly, I somehow managed to get a dead mob beyond the border and it stayed in the death animation. I tried this on three worlds with Cows, Sheep, Mooshrooms and Cats and it worked semi-consistently, with variation based on entity pushing and spawn egg randomness. 

These aren't super pressing bugs, as old worlds really don't matter a lot, but since old worlds are a feature it'd be nice if they worked bug-free.

Thanks for reading!