Ron Guth: The 1868 Two Cent piece is similar in rarity to the 1867. The only varieties worthy of mention are a misplaced date (with a possible 6 protruding from the denticles beneath the 6 of the date) and a possible 1868/7 overdate (subject to further confirmation).
Sources and/or recommended reading:
"Getting Your Two Cents Worth" by Kevin Flynn
"Two Cent Piece - An 1864 Attribution Guide" by Frank Leone
"Cherrypickers' Guide, Fifth Edition, Volume I" by Bill Fivaz and J.T. Stanton