Parshas Emor is addressed primarily to detailing the special halachos of kohanim and yomim tovim (festivals). It would seem that these two themes form the bulk of the parshah due to their similarity. Kehunah (Priesthood) and yomim tovim are compared insofar as they are endowed with legal kedushah status. That is to say, unlike personal kedusha elaborated upon in Parshas Kedoshim, which is an individualized state attainable by one's actions and closeness to Hashem, the kedushah of Parshas Emor is an objective status regardless of the merits. Thus, a kohen has kedushah of kehunah even if he does not rise to spiritual heights, and the yom tov days are likewise endowed with holiness, even when not observed. It follows that the Torah placed the kedushah of Emor after that of Kedoshim as part of its overview of the varied dimensions and types of holiness.
However, Parshas Emor features a very unusual story (per Rashi from Medrash Vayikra Rabbah), in which a man whose father was Egyptian and mother was Jewish wished to set up his residence as part of the tribal formation of Dan. When he was instructed that he cannot, as tribal relationship goes according to patrilineal rules, he blasphemed. (See 24:10-23.) Why is this event contained in this week's parshah?
It would seem that the blasphemer acted not out of sheer anger. Rather, he was frustrated about his status and/or its ramifications. He argued that it was not fair that he - out of no fault of his own - was penalized by not being able to join the tribal formation he desired. To put it in broader terms, the blasphemer objected to God's endowment of objective halachic categories - whether they be those of kedushah (such as in the case of kohanim, etc.) or yichus (lineage). He argued that only subjective, personal attainment should count. This is the connection between the story of the blasphemer and the themes of objective kedushah, as exemplified by yom tov and kehunah.
It is noteworthy that when Hashem taught Moshe the punishment due the blasphemer, He included the rules for harming people and animals as well. (See end of parshah.) Why?
As explained, the blasphemer objected to God's rules. On a deeper level, the blasphemer was judging God, and the curse uttered was thus not merely a harsh reaction of rage, but a verbal assault, as if the blasphemer wished to harm or punish God, so to say, for creating Torah laws as they stand. The blasphemer wished to "alter" God, as he was unsatisfied with His laws. Thus, "gidduf" - blasphemy - is very much like an assault, and the halachos of assaulting person and animal are thus taught alongside it.
Right before the story of the blasphemer, the Torah presents the halachos of the menorah and lechem ha-panim ("show-bread"). Chazal understood the menorah to represent God's Presence, and the shulchan (table) which held lechem ha-panim as reflective of God's sustenance. (See Rashi at beginning of Parshas Terumah.) These two themes are the Torah's reply to the blasphemer. We are told that God is with us, supervising us and providing all that we have. Despite whatever status situation we are in, it is Hashem's will, and it is just. However, Hashem's personal care for us, and our ability to be close to Him, are always the same, and He placed us in whatever situation we find ourselves as part of his special, objective, personally-tailored master plan.