Is there any way, using deckbox or another resource, that one can find out what card(s) are keeping a deck from being a specific format?

http://deckbox.org/sets/498818

This is a simple, cheap deck I threw together for some casual play, and it comes up as being a "Complete {swamp} Deck", while many of my other decks come up as "Legacy" or "Standard" decks.

It would be nice if there were a quick way to determine what is holding a deck back from being a particular format, in the event that someone would like to modify their deck to play in a tournament that only allows certain formats.

There isn't really a way to just know which card(s) are causing a problem unless you're familiar with which sets are legal in standard or modern (all sets are legal in legacy and vintage). At current, your deck is mostly standard with a few cards that have just rotated, which means it's technically a modern deck. At least one other person has pointed out the fact that the deck legality isn't working properly to Sebi so, with any luck, it'll be fixed with Sunday's update.

That being said, the cards preventing you from being standard legal include:

Vampire Nighthawk, Victim of Night, and Disentomb. Nighthawk (how we miss it so!) and Disentomb are from M13 and Victim is from Innistrad. The entire Innistrad block and M13 rotated with the official release of Theros.