Timing. The traditional "first thing" slot means that you set the tone and catch children alert and receptive. But by the same token you use up productive classroom time.
Do all the staff always come in? It's important that they take part and absorb the values. But on the other hand they could use the time for planning.
Who takes assembly? Are there any staff who refuse not out of conviction, but from sheer stage fright? Perhaps we should help and encourage them.
Do the children enter and leave silently, to peaceful music? Many primary headteachers would love to know how that can be achieved.
Do any children miss assembly? It can become a convenient time to keep children for extra reading, or an instrumental lesson. Ofsted teams sometimes query this practice.
If you're a church school, does the vicar or the priest take assembly? Sometimes he or she could use some help but it can be hard to offer this diplomatically. Again, ideas welcome.