In chapter 22 of The Scarlet Letter, what does the order of the procession reveal about the priorities or values of the Boston community?
The answer to your question can be found in the way that Hawthorne describes the feelings of the typical villagers. He explains that, although they are probably forth or fifth generations away from the earliest settlers, they still have a sense of belonging in relation to how their ancestors witnessed the class division in the United Kingdom. Namely, that soldiers were to be revered, and that those in leading positions would be also revered even more so than the soldiers simply because they hold the authority bestowed upon them by God.
The people possessed, by hereditary right, the quality of reverence; which, in their descendants, if it survive at all, exists in smaller proportion.
This means that, even though the reverence given to social superiors is not as eccentric as that which was given to them in the old days in England, the villagers still possessed that trait.
Moreover, Hawthorne explains that the soldiers carried themselves on haughtily but that they were first in the procession perhaps as an opening act that is followed by an even haughtier and more flamboyant group: the aldermen; the leaders of the community. In Hawthorne's words, the aldermen
...showed a stamp of majesty that made the warrior's haughty stride look vulgar, if not absurd. It was an age when what we call talent had far less consideration than now, but the massive materials which produce stability and dignity of character a great deal more.
Hawthorne goes on to explain that these people have a tendency to award their respect to those who have "fortune and self-reliance" rather than wits and academic attainments; not even the soldiers get as much pomp as the elders. In fact, the soldiers are called the "military escort" to the elders who definitely carried themselves more arrogantly than the soldiers. The villagers do not go with those who fight or sacrifice, but place more importance on whoever has the capacity to make them feel safe.
Hawthorne compares this behavior to the behavior displayed by the first settlers and how they chose their leaders. He describes the forefathers of the nation as "rogues" who were not necessarily bright, but that their ability to make others feel safe, and as part of a group, is what instilled the respect from others. Behind them was Dimmesdale, who was to take the center-stage with this Election day sermon. However in this case we know that he is already highly acclaimed and adored simply because of his talent for speech, his youth, his (former) looks, and his so-called righteousness.
What this shows is that the military were deemed not as importantly as the elders. They, in turn, still are not as highly revered as Dimmesdale.