My sister was divorced back in 2002 and originally had custody of her son. Her ex husband was able to get custody of him shortly after that because my sister was late bringing the child to a designated meeting place where her ex husband was picking him up for visitation. They live in two different states and he had a lawyer. To make a long story short, he got custody in 2007 and has had the child ever since. My sister recently discovered that the custody papers were never filed.. the only ones filed were the ones from 2002 when they got their divorce. So the question is... what happens if the custody papers were never filed by his lawyer? The court date did happen, however, the papers are not filed. Does this mean that they have to go by the last set of papers on record that were filed in 2002 in which my sister had custody?

Basically yes. If there are no signed current order that supersede the ones from before then the old ones would take precedent.

But how did all of this "change in custody" happen, if nothing was filed, how did one parent get custody of the child. Was it all done in the same court,

...The court date did happen, however, the papers are not filed. ...

What "papers"? Do you mean that the lawyer forgot to submit an order for the judge to sign?

He obviously has a problem. If it's a backwards court like here, there may be no record of what happened and the judge may not remember. However if it can be proven what was decided, it will be a simple matter to get the judge to sign the order once one is submitted.