In 6:38 Allah says that he/Qu'ran has not left out/neglected a thing.
is that not a statement of the Qu'ran as a complete source?
You will notice the Qur'an does not tell us how many rakats (units) in each prayer, what percentage of zakat to give, etc. So people who use this ayah to justify their stance on not following the sunnah, as recorded in the hadeeth, then see that the question doesn't make sense. The ayah does not mean that everything, every detail of Islam, every detail of life, of the world is recorded in the Qur'an.
The Qur'an is a complete guide in that it directs us where to go for all the details. So many verses on obeying the Prophet (may the peace and blessings of Allah be upon him). Allah taught the prophet the details of Islam that are not in the Qur'an, gave details for some parts which are.
This is one translation of the verse you gave the reference for:
There is not a moving (living) creature on earth, nor a bird that flies with its two wings, but are communities like you. We have neglected nothing in the Book, then unto their Lord they (all) shall be gathered.
One interpretation is that the Book here is not in reference to the Qur'an but the preserved tablet that has recorded on it everything that will occur up until the Day of Judgement. This is similar to Surah Hood, ayah 6.
If one takes the Book to refer to the Qur'an, this does not imply that the sunnah is not an authority and obligatory upon Muslims to follow. As we all know, the details concerning the prayer, zakat, fasts etc are not all spelled out, detailed, or explained in the Qur'an. So, in order for this interpretation to be accurate, given the reality of the situation, it must mean the following as ibn al-Jawzi explained it: "It is a general statement that has a particular intent behind it. The meaning therefore is: We have not omitted anything which you would be in need of except that it has been made clear in the book, either by clear text, undetailed statement, or indication." In other words, everything is mentioned in the Book, in either direct detail, or by reference to the source where the necessary detail can be found. Hence the Book itself does not contain details of the prayers, fasts and so forth, but the Book points the believer to where those details can be found: the sunnah of the Prophet . When understood in this manner, such verses are not an argument against the authority of the sunnah (or it's records in the hadeeth), but rather it's indispensability.
Clearly Allah does not spell out all the details of worship, law and life in the Qur'an itself. Instead, the Qur'an points the believer to all that is needed to be truly guided. Included in this is the sunnah itself as well as other aspects such as contemplating creation and so forth. The Qur'an clarifies all that is needed in one's life and part of what is needed in one's life is adherence to the sunnah of the messenger of Allah . The Book itself makes this fact abundantly clear with it's numerous verses containing the command to obey the Prophet . When we follow the Qur'an we are following Allah's words and command, as not a word of it is from the Prophet . To obey the Prophet we must follow his sayings, commands, actions, as they are recorded in the hadeeth. There is no more accurate record of the sunnah, than their preservation in the authentic hadeeth.
The sunnah of our beloved prophet is preserved down to the minutest detail in the authentic hadeeth, which is only proper if he is the last prophet, sent for the whole of mankind until the end of time, after whom no prophet will come. Otherwise the verse telling us that we have in the Prophets example a beautiful pattern of conduct for us, is meaningless.
If a person believes that nothing other than the word of Allah is to be considered, and any explanation by the Prophet is invalid, or that all explanations by him cannot be relied upon wholesale, in essence this is implying that Allah, instead of sending His book through a Prophet, could have sent printed copies directly to each individual, if it's explanation by the Prophet was not necessary, and if each individual had to use his/her own personal reasoning as it's explanation. It's implying that if He knew with His knowledge of the future that the records of the prophets explanations would be wholesale rejected and classified as corrupt, then He got it all wrong by sending it through a prophet and asking the prophet to explain it for mankind. But Allah did not leave us to fumble in the dark making our our own explanations, he sent the book to a prophet, described in the Qur'an as a mercy for all mankind, to show us how to put it into practice, to explain it to us, to show us the details for certain things mentioned without detail in the Qur'an etc. Allah was indeed was merciful to us in leaving us such a rich and detailed source of the explanation of the Qur'an, it exegesis, and in the Prophets character and practices, so that we can follow his example.