syntax for recording completion date

If I've understood correctly, you're looking to set 'Actual Build Completion Date' to the current date when checkbox 'Build Complete' is checked. If you use a formula field - something like If([build complete]=true, Today()) - the field will contain the current date, not the date when the checkbox was checked. You could use a form rule or a pipeline to set the date - I'd suggest using a pipeline as it can be triggered from any record update (from a form update and a grid edit update).