Why did God command Noah to take seven each of the "clean" animals on the ark? Is this evidence that the sacrificial system was in play? Why did God make a distinction between clean and unclean to Noah?
As pointed out in a number of commentaries (such as Rav Hirsch and Art Scroll for example) the "clean" animals were those that were allowed to be sacrificed even before Noah and his children were allowed to eat meat. One of the explanations for 7 is that the seventh (unpaired) animal is the one that was to be sacrificed. Other commentaries state that it was supposed to be seven pairs of clean animals to allow for male and female sacrifices.
Rav Hirsch states that one of the reasons for the kosher laws given later is that the Bnai Yisrael were to be an Am Kohanim (nation of priests) and as such were only allowed to eat those animals that were allowed to be offered on the altar of Hashem (by Noach and his descendents). Note that the animals sacrificed by Bnai Noach were not restricted to the animals that Bnai Yisrael could sacrifice. According to Rav Hirsch, any animal that is kosher for Bnai Yisrael to eat (after the giving of the Torah) was allowed to be sacrificed by Noach (even for example a deer or a giraffe).
Also see the answers to How many Kosher animals were in Noach's Ark?
I would like to input my thoughts to this discussion; Moses is writing this book and is not describing for us modern readers. He is giving an account and what the people of Israel new what was food to eat, not all animals are considered food except for the one's YHVH described. An animal that is considered food had to go through a procedure before being considered clean or defiled depending how close they followed YHVH's instructions. YHVH would have told Noah what to sacrifice just like he must of told Adam because he was covered in animal skin himself and Cain did not sacrifice what he was to do and many others did not obey which began the downward spiral of destruction. Just as we see in the beginning how YHVH created the sabbath day to keep and had to let Israel know it again. YHVH had to tell Abraham but it doesn't mention that he did.