I experimented a bit with this and here is what I've found:
Dropped items can be found when a data value is not specified.
/scoreboard players tag @e[type=item] add stone {Item:{id:"minecraft:stone"}}works without issues.
When a data value is then specified, the command no longer works, and gives an error message saying the item did not have a matching data tag.
/scoreboard players tag @e[type=item] add stone {Item:{id:"minecraft:stone",Damage:0}}does not work.
This holds true for all dropped item entities.
You search for an int named Damage, but it's a short, not an int.
Testing for data requires the correct data types.
Use