In 1x08, Lexi says she tried Stefan's diet, and lasted two weeks. In Bloodlust (the second book in Stefan's Diaries, which is BASED off the show) Lexi says that she only drinks animal blood, and is mentioned drinking both fox and goat blood.

In 1x09 Stefan said he was the last to see Katherine before she was taken, but in 1x13 Damon was seen rushing in the room where Katherine was shouting "Don't take her!".

In 1x20 Damon said he woke up (after death), didn't know where he was, went to the church, and watched them take Katherine inside. In 2x04, Katherine is seen on the rode where BOTH Damon and Stefan still lay dead, after the church fire. (probably much after the fire)

In 1x21 Isobel said Katherine tracked her down, but in 2x11 Katherine said Isobel found her.

In 2x06, Jenna stabs her stomach with a knife (courtesy of Katherine). In 2x11, she and Alaric are caught by Elena after sex. Um... not much time could have possibly passed between the episodes. She SHOULD NOT have been sexually active again yet.

These are a few, but there are probably more. It just... it annoys me to think that a show contradicts itself so much.