Is it okay to tie all the DIN ground connections together? Is it okay to do the same with the DOUTs? Is it okay to connect DIN grounds to DOUT grounds?
No problem. There is only one common ground for all DINs and DOUTs.
Raphael
Why [tha hell] do we need all that ground pins & wires?!
We can just ground the ground from the core to the casing and do the same with dout/din/ain/lcd/etc…
Because ground loops are bad, mkay 
We can just ground the ground from the core to the casing and do the same with dout/din/ain/lcd/etc…
no one keeps you from doing that, but if you ever got a problem inside a small box, you’d know that it’s sometimes better to have some unpluggable and removeable single items in it.
next point is, that not everyone is using a metal case…