If in the invoice module, custom date select fields are created below the product / line items, the date select is precisely displaced by the amount of space needed for the products / line items. See screenshots.
Edit: It seems that the first time the date window is called, its location is saved for future calls. So if I select all the line items first, then select a date location it is perfect. If I remove some line items then, then the date pop up is below where it should be.