Rav Moshe explains that the oil for the מנורה needed to be pure teaching us that people who are role models and teachers of תורה need to act in a completely pure way. Rav Eliezer Ginsburg explains that אתה תצוה…שמן זית זך teaches us that each and every Jew needs to try and make themselves pure from bad מידות.
Some thoughts on the Kohen Gadol and his garments: 1) The חושן is a כפרה for judgments that are not so correct and the אפוד is a כפרה for עבודה זרה. Rav Moshe explains that this explains why the חושן and אפוד were connected. When someone does incorrect judgement, for instance, when in business a person might cut some corners judging that what he is doing is actually ok, he is in essence denying the fact that ה׳ runs the world and therefore doing עבודה זרה. 2) Rav Moshe Shternbach explains that even though the כהן גדול was on such a high level he still had to wear the חושן with the names of the Jewish People on it. 3) The כלי יקר explains that the אפוד is called מעשה חושב because it was a כפרה for עבודה זרה and even thoughts of עבודה זרה need כפרה. 4) The names of כלל ישראל are both on the חושן on the heart of the כהן and on the אפוד on the shoulder of the כהן to show that the כהן גדול needs to bare the burden of כלל ישראל in his heart and lift them up on his shoulders. Rav Elias says that it means that the כהן גדול needs to help out every Jew, not just think about them. 5) The ספר החינוך explains that the כהנים wore special clothing so that they would feel dignified in their position. Rav Moshe Shternbach explains that it was so that בנ״י would be in awe of the כהנים. 6) The Shach and the Alshich say that there is one bell and 2 pomegranates because it is better to listen than to do the talking. Furthermore, the bell was made of gold which makes less noise than other metals because even when you do speak it should not be audacious. 7) On the ציץ it says קודש לה׳. The חתם סופר says that עזות מצח, brazenness, comes from the forehead, so he writes קדש לה׳ to show that the only time one can be brazen is when it is for the sake of ה׳.
The חתם סופר quotes the חובת הלבבות to explains that the reason why ה׳ commanded to take the חכמי לב אשר מלאתיו רוח חכמה is because He wanted them to use their potential for the good. The פסוק says ״תדבר אל כל חכם לב אשר מלאתיו רוח חכמה״ meaning that to make someone into a חכם לב, tell them how filled they are with רוח חכמה. The רל״ג explained that מלאתיו is לשון יחיד to teach us that each of them shouldn’t think that they are better than the next guy.
The ספר מאוצרינו הישן says that the reason why it first says that ה׳ will dwell amongst us and then it says that he will be our God is because once He dwells among us and we see how amazing that experience is then we will want Him all the more to be our God.
The אור חיים explains that כתית למאור teaches us that the more בנ״י get squashed the more light comes out of us. Rav Moshe Shternbach explains that it means that we need to squash ourselves for תורה, but not למנחות, not for פרנסה. Rav Moshe Shternbach explains that מנחות don’t need שמן זית זך because they are not totally לשם שמים since we get הנאה from eating them, but the מנורה is completely לשם שמים and therefore needs to be pure. The כתב סופר says that we crush the olive oil for light, which is תורה, but not for מנחות which is פרנסה. Another פשט is that we shouldn’t crush ourselves over מנחות, which is relaxing and vacation. In contrast, Rav Berel Povarsky says that the olive oil needs to be crushed because the only way to grow in תורה is to crush yourself over it.
The גר״א explains that the פסוק says פיתוחי חתם קדש לה׳. The word פיתוחי is like מפתח. The גמ׳ says that 3 keys are given to ה׳ only: giving birth, resurrection of the dead and rain. Those 3 things start with the letters ״ח״, for חיה, and then ״ת״, for תחיים המתים, and then ״מ״ for מטר. That spells חתם, so the פסוק is teaching us that the 3 keys of חתם are only קדש לה׳.
The מלאכת מחשבת says that משה didn’t even need to explain to אהרון and his sons what to do. All he said was ״הקרב״ and they automatically knew exactly what to do.