Or HaChaim on Leviticus 8:10/אור החיים על ויקרא ח׳:י׳

1וימשח את המשכן, He anointed the Tabernacle, etc. Why did the Torah interrupt the report of clothing Aaron in the priestly garments and his being anointed with the report of the Tabernacle being anointed? The reason is presumably that the Torah had reported that Moses was commanded to anoint the Tabernacle before it reported that he had been commanded to anoint Aaron (compare Exodus 40,9). You may argue that it would have been appropriate then for the Torah to report the anointing of the Tabernacle before reporting the dressing of the priests in their garments in order to conform with the order in which the Torah reported the commands as being issued by G'd. The reason Moses did not do so may be found in a detail in verse 2 where G'd had said to Moses: "take Aaron, his sons, the garments, and the oil of anointing." If the anointing of the Tabernacle had been intended to precede the sons of Aaron being dressed in their priestly garments, the Torah should have written as follows: "take the oil of anointing, etc." seeing the Torah wanted the first command to be carried out first. If the Torah had written verse 2 in that order we could not possibly have mistaken its intention. Seeing the Torah first mentioned Aaron, it is clear he was to be anointed first before he was to put on the priestly garments. It was not possible to misinterpret what G'd wanted because the Torah had already said in Exodus 28,41: "dress your brother Aaron and his sons in them and anoint them." It is clear therefore that the Torah intended to have the priests put on the priestly garments prior to anointing the Tabernacle with the oil of anointing. Why is it then that in פרשת פקודי the Torah reported the anointing of the Tabernacle before it reported Aaron being dressed in his priestly garments? We may answer that seeing the Torah did not want to interrupt between the act of Aaron's' getting dressed and being anointed, it wrote all the laws pertaining to Aaron consecutively; this did not mean however, that the anointing of the Tabernacle was to be preceded by anything but the anointment of Aaron himself. This is the point we learn from the sequence of the Torah's report in our chapter.