There is a good explanation here http://learnenglish.britishcouncil.org/en/english-grammar/verbs/verbs-followed-that-clause

The word THAT is a very, very common word in English. It can be a pronoun, and adjective, or a conjunction. I won't go into all the details. The easy answer to your question is, both sentences are correct. In the sentence, "I know I'm wrong", the word THAT is implied.

'That' is when you talk about something far. Further than 'This'. 'This' is about something near.

Well, I think both examples are correct, the "that" in the second example is just not necessary. If you're not sure wether you should put it or not, just put it, it wouldn't do you wrong!