What not to Do in Taraweeh:-

1.) Should not look forward for its conclusion, should be done with Kushoo
Allaah says (interpretation of the meaning): "Successful indeed are the believers, those who offer their salaah (prayers) with all solemnity and full submissiveness." [al-Mu’minoon 23:1-2] i.e., fearing Allaah and in a calm manner. Khushoo’ means calmness, serenity, tranquillity, dignity and humility. What makes a person have this khushoo’ is fear of Allaah and the sense that He is always watching. (Tafseer Ibn Katheer, Daar al-Sha’b edn., 6/414). Khushoo’ means that the heart stands before the Lord in humility and submission. (al-Madaarij, 1/520).
It was reported that Mujaahid said: "and stand before Allaah with obedience" [al-Baqarah 2:238 interpretation of the meaning]’ part of obedience is to bow, to be solemn and submissive, to lower one’s gaze and to humble oneself out of fear of Allaah, may He be glorified. (Ta’zeem Qadr al-Salaah, 1/188).

2.) Should not be fast

Narrated Abu Huraira:
Once the Prophet entered the mosque, a man came in, offered the prayer and greeted the Prophet. The Prophet returned his greeting and said to him, "Go back and pray again for you have not prayed." The man offered the prayer again, came back and greeted the Prophet. He said to him thrice, "Go back and pray again for you have not prayed." The man said, "By Him Who has sent you with the truth! I do not know a better way of praying. Kindly teach Me how to pray." He said, "When you stand for the prayer, say Takbir and then recite from the Qur'an what you know and then bow with calmness till you feel at ease, then rise from bowing till you stand straight. Afterwards prostrate calmly till you feel at ease and then raise (your head) and sit with Calmness till you feel at ease and then prostrate with calmness till you feel at ease in prostration and do the same in the whole of your prayer."
Bukhari :: Book 1 :: Volume 12 :: Hadith 759

He (saw)"forbade three things: pecking like a hen, squatting (iq'aa'), like a dog and looking around like a fox"
Ahmad and Abu Ya`laa. See Saheeh at-Targheeb (no. 556).

3.) Reciting Qur'an fast, so that no one behind understand and the reciter just want to finish reciting..