If there are "phantom" invoice data then try to see which sales order it is related to and see what happened to the sales order.  You might need to extract the data using Excel.  How did you find the data?  

We can see it when looking at Inventory Module -> Item Inquiry. The quantities down at the bottom shows qty 4 "In Shipping". There are no open sales orders with that item on it, looking on the "orders" tab in item inquiry. Also running the "open sales orders by item" report in sales order module for that item will show no orders. Also I've closed out and posted all batches in AR invoices, Sales Order invoices, and Sales Order shipping data entry.

I can't figure out where to look next or how to figure out what's causing the qty 4 to be stuck in shipping.

We can see it when looking at Inventory Module -> Item Inquiry. The quantities down at the bottom shows qty 4 "In Shipping". There are no open sales orders with that item on it, looking on the "orders" tab in item inquiry. Also running the "open sales orders by item" report in sales order module for that item will show no orders. Also I've closed out and posted all batches in AR invoices, Sales Order invoices, and Sales Order shipping data entry.

I can't figure out where to look next or how to figure out what's causing the qty 4 to be stuck in shipping.

"In Shipping" means invoice data, not an SO.

Use Excel to query the two raw data tables I mentioned above.

You can also try the "Rebuild Sort Files" utility (SO & IM modules) but I am not sure if that will help with this issue.

In item inquiry the panel you are looking at is based on sort files and as Kevin suggest rebuild them and see what happens.