The things you should do after Falcon's dthrow (really, after anything you do with Falcon) are either to watch what your opponent does when you hit him, and react accordingly or to read (predict) his next action, acting accordingly.
There aren't any guaranteed follow-ups from a dthrow (that I know), but there are some examples:
>if your opponent DIs upwards and airdodges towards you, you can charge a down smash and land it for a hard punishment.
>if you think that your opponent will DI away and shield on ground, you can dash and grab them to reset the situation.
>if your opponent doesn't have a quick reaction or his character doesn't have much to hit while you're below him, you can quickly short hop and try to follow with an uair.
Really, as Brawl has little hitstun, none of these options (and anything one can think) are completely safe, if that's what you asked.