What are the downsides of using a LM7805 with a 11.1v Li Ion Laptop battery to charge a USB device?
Disadvantages of 7805 in this application as already noted by others: Wasting a lot of heat, draining battery twice as fast as you might otherwise.

DC-DC converter might be a good off-the-shelf solution for you:

500mA $2.84
http://www.digikey.com/product-detail/en/R-78E5.0-0.5/945-1648-5-ND/2834904

1 Amp $7.49
http://www.digikey.com/product-detail/en/R-785.0-1.0/945-1038-ND/2256218

Hope that helps.