What details of the "witch-meeting" parallel those of a church communion service?

Simply put, the details imposed in the witch-meeting is parallel to communion because of three reasons.

First, the whole congregation is gathered together.

Second, communion is usually considered to be a very serious and solemn time, often accompanied by a mournful hymn, such as what is being sung in the short story.

Lastly, communion is a time to focus on and remember your sin. In Young Goodman Brown, the dark figure reminds the protagonist and his wife about the sin present in all people.