What you are seeing is a few things, but none of it is a doubled die.
On Liberty you the left side you are seeing DDD (Die-Deterioration-Doubling) This happens as the die ages, it affects the fields on the direction of the closest rim. On the left is the closest rim, on the date is flows to the right. And on the motto you will see this on the tops of the devices. Here is a classic view of this:
Note the distortion is on the fields and not on the devices. We see this on the single squeeze dies more than on the older dies. On the older dies the devices show the die wear and they move towards the direction of the rim. Same also on the bust, or it could be from over polishing of the die. Because the bust is a wider opening on the die, it can allow the polishing to fall into the void on the die, removing part of the busts incuse die edge. With the metal removed, it makes a raised area on the coins.
On the reverse we see you denoted one of the design elements that I refer to as a false column. There are 4 of them on the column areas:
Why are they there?
There are on the areas of the building were colums are behind those areas. Making a 3-D effect on the design. The false column are weaker that the full 12 columns. So they eventually get reduced or totally removed.
Under ONE is the same thing mentioned earlier, DDD.
Hope this helps. Your coin is not a premium coin, but an educational piece. You might want to save it to show to a new collector you run into.