And it came to pass on the eighth day (Lev. 9:1)
The eighth day of the consecration of the Tabernacle was the first day of the month of Nisan. Ten special events took place on that day, including many "firsts": Nisan became the first of the months when counting the months of the year; the priests, not the first-born, performed the special services; communal sacrifices were brought; the priests blessed the people with the Priestly Blessing. (Breishit Rabba)
Aaron lifted up his hands to the people and blessed them (Lev. 9:22)
Why did Aaron, not Moses, bless the Jewish people? The Divine Presence could only rest in the Tabernacle after the sin of the Golden Calf was atoned for. Aaron was the one who had to effect the atonement, as it was he who was ultimately responsible for the sin having been committed in the first place. Therefore, he was the one to bless the people. (the Rebbe)
And they [Nadav and Avihu] brought near before G-d a strange fire which He had not commanded them (Lev. 10:1)
Although Nadav and Avihu were great and holy men who brought the fire upon the altar for the sake of Heaven, it was considered a sin because they did it on their own, without having been commanded to do so by G-d. No matter how great one's intellect, it must be subservient to the will of G-d and to His commandments.
When a Jew does a mitzva, even if his intellect cannot grasp the reason for doing it, and he performs it solely because it is a Divine command, the mitzva will give him strength and elevate him spiritually. (Chidushei HaRim)
All that goes on its belly (Lev 11:42)
Comments Rashi, "this is a snake." A person who is haughty and acts condescendingly toward others should consider what happened to the snake in the Garden of Eden: before it was cursed it walked upright like a human being; after it behaved arrogantly toward its Creator, it was humbled and made to creep through the dust... (Maayana Shel Torah)