Achare Mot

Mishna in Shavuot (Chpt. 1) lists the Kapara (atonement) for different Averot (sins) done by Kohanim as well as regular Yisraelim. In doing so, Minsha picks a very interesting order. 

When it comes to the Yisraelim the Mishna lists the Kapara for sins related to the Mikdash first and only after it goes on to list the Kapara for other sins. The obvious question is, the order should be the exact opposite. The majority of the Mitzvot performed by the Yisraelim are done outside of the Bet Hamikdash, so the Kapara related to those sins should be listed first. And when it comes to the Kohanim, the Mishna lists the Kapara for the sins done outside of the Mikdash first and only afterwards it lists the Kapara for sins related to the Mikdash. Kohanim's primary service is in the Mikdash and the Kapara related to those sins should be listed first. 

Sefer Shem Mishmuel offers the following principle in order to answer the question. When a person starts the process of spiritual growth, first one should start fixing the sins that are easier to fix and only later in the process one should engage in fixing the sins that are harder. According to this principle, naturally Kohanim do not stumble on sins outside of the Mikdash as much, since most of the Mitzvot they have are performed in the Bet Hamikdash. Therefore, it's easier for them to start fixing the other sins first. Sins related to the Mikdash are much more common and harder for the Kohamim to fix. As a result, for the Kohanim the Mishna starts listing the Kapara for the other sins and only after the Kapara for the sins related to the Mikdash. As opposed to the Yisraelim, whose primary Mitzvot are done outside of the Mikdash, it's easier for them to start fixing the sins related to the Mikdash first. Those sins are not so common for them.