When the form is being complete you could use the Event for After Update
NO NO NO!!! The Form's AfterUpdate event runs AFTER the record is saved. Updating the record at this point is like the old saying about closing the barn door after the horse has escaped. But this is worse since it puts Access into an infinite loop. Luckily, newer versions of Access will recover from this infinite recursion - record saved, you dirty it by changing a value, record saved, you dirty it, etc.
The correct event to use is the FORM's BeforeUpdate event. This is the last event that fires BEFORE the record is saved. It is the event you would use for final validation so you can cancel the save if there are any errors. It is also appropriate to use this event to timestamp the changes.
Although a default of Now() works for newly added records and so no code is required, there is no default if you want to stamp updates so you will need a line of code.
Me.LastUpdateDate = Now()
If I show this field on the form (which depends on the user's preference), I set it's locked property to Yes and TabStop to No. Since you are managing the timestamp in code, you don't want someone to modify the date and time manually.
In one of the earlier posts in the thread, you put the Me.LastUpdateDate = Now() into the AfterUpdate event of the LastUpdate control. Think about the logic of this (I know it all seems pretty random in the beginning but there really is logic behind how things work). If this event fires AFTER a field is updated, you would need to actually update the date in the control to fire the event and trigger the code. And since you want this field to be populated automatically, it wouldn't make sense to put the "automatic" code in this event.