1. The first digit of the date was placed into the master die prior to making any hubs or dies. This means that if there was a zero as the first digit of the date on ONE coin, ALL of them would be like that.
2. Your coin dealer is a quack who has no clue what they are suggesting. Sending this damaged coin to a grading service would be a complete waste of your time and finances. Obviously the dealer doesn't care about that.
3. HOW the damage occurred to your coin? Well there is no way of telling exactly what caused it, but HOW is a different story. The 1 digit on your coin was scraped off to one side by something that had a lot of force behind it. It was scraped from left to right. The curved pile of stuff to the right of the normal 1 is most of the relief of the 1.
4. When trying to determine whether something is - or is not - on a coin, take into account the surrounding area of the detail that caught your attention. If you direct your attention to the vest and bow tie area you will see a lot of damage in that area that is certainly directly related to the damage on the 1. This is part of the deduction process that has to go with every coin attribution. If you are going to collect die varieties or errors, this simple deduction process needs to become a part of what you do when looking at coins.