I am looking for ways to reduce filesize and overhead in a large
spreadsheet, and as part of that I'm looking for alternatives to array
functions. I wrote this code thinking I could determine when an array
function occurs:

Dim rCell As Range
For Each rCell In ActiveSheet.UsedRange
If rCell.FormulaArray = True Then
MsgBox rCell.Address
End If
Next rCell

.... but this seems to find a cell that is part of an array. Can anyone
suggest some better code to determine if a cell contains an array
function?

Thanks

Try
If rcell.HasArray = true then

.... instead.