Active player has 0 cards in hand and flashbacks Faithless Looting. He dredges two cards, but he notably out of order sequences when he dredges and placed the dredged card into his “hand” (face-up pile on the table) and then one by one flips cards from his library into his graveyard. He begins to dredge a third card; places a Stinkweed Imp into his hand pile and flips over two cards; then his opponent stops him and calls for a judge.

The active player does not know the location of any particular cards in his deck. Format is Legacy, and the deck does not need the player to rearrange cards from the dredge, so the order of the extra card milled is known to both players.

I thought at first thinking GRV, which on confirmation with another judge, who I believe I did not communicate the exact scenario properly, told me to consider LEC. Appeal occurs and HJ rules DEC with downgrade, but he decides to place the two revealed cards back on top the library and asked the player to shuffle his library.

Upon further analysis I understand DEC with downgrade as his first illegal action was to place a card illegally into his hand. The two milled cards are a sticking point. DEC with downgrade doesn't have a shuffle in the fix. I am just curious to what other judges think of this scenario.

The way I see it we either have a GRV as you thought for changing the order of your graveyard in a format where it matters or DEC as your HJ rules, what I don't agree with on the DEC line is where your HJ ruled it if we class the players hand being the two cards he pulled out of his graveyard at “to dredge” then at that moment is when the first wrong card has been drawn so we should rewind back to that point.

As for the DEC fix, I agree the shuffle shouldn't have happened they should have just been left on top

There are two infractions here: DEC and LEC.

From IPG, 1.3 Applying Penalties:

Separate infractions committed or discovered at the same time are treated as separate penalties, though if the root cause is the same, only the more severe one is applied.

So you apply the penalty for DEC (since it's been downgraded the penalty is actually the same here), but you still have two infractions at hand and you apply the relevant fix to both of them.

DEC -> dredge card back in the graveyard
LEC -> shuffle the illegally revealed cards into the library (taking into account globally known parts of the library itself - due to some Terminus or whatever)

Well said, Andrea!