Examples of Unobvious mistakes:

• Not being totally exact with the elongation of letters: (Making the Madd shorter or longer by a 1/2 or even 1/4 degree etc.)

• Not observing the attributes of each letter perfectly: (Slightly rolling the Raa', or exaggerating the 'N' sound in Noon etc.)

• Not observing the rules with which to pronounce letters when they are next to each other (like not merging certain letters that should be merged (idghaam) and not clearly pronouncing those which should be clearly pronounced (ith-haar) etc.)

• Making light letters sound heavy and heavy letters sound light (Except if by doing this you change a letter into another; in this case it would be an obvious mistake.)

And of the proofs that the scholars bring to show the obligation of Tajweed and that it is an established Sunnah is that Allah says in the Qur'an, the meaning of which is:

'And recite the Qur'an (aloud) in a (slow and melodious) style (tarteela)' (Surah Muzzammil, aayah 4)

Ali ibn Abi Talib (radi Allahu 'anhu) said in the explanation of this aayah:

"at-Tarteel is Tajweed of the letters and knowing where to stop (correctly)".
And of the proofs also is that Allah says in the Qur'an, the meaning of which is:

'Those who We have given the Book to, give it its right in recitation ( recite it as it should be recited)' (Surah al-Baqarah, aayah 121)
And of the rights of reciting correctly is reciting it the way it was revealed.

There are various ahadeeth also showing us the importance of Tajweed.

Umm Salamah was asked about the recitation of the Prophet (sallallaahu alaihi wa sallam) and she described it as a recitation 'clearly-distinguished letter by letter'.

Sa'eed bin Mansoor relates in his Sunan that a man was reciting the Qur'an to Abdullah bin Mas'ood and he recited
"Innamas sadaqaatu lil fuqara-i wal masaakeen", so Ibn mas'ood said: "This was not how the Messenger of Allah (sallallaahu alaihi wa sallam) recited it to me!" So the man asked,
"How did he read it to you oh Aba Abdir-Rahman?" So he said "Lil Fuqaraaaa-i wal masaakeen", he elongated the word Fuqaraa and the knowledge of the different lengths of elongation (mudood) is also from the rules of Tajweed.