The problem is basically due to the fact that the monday formula evaluator returns an error when any part of the formula is invalid, even when that portion is excluded. Specifically,
WORKDAYS({Timeline#End},{Completion Date})-1 returns an error whenever either of the dates is blank.
To fix it, you have to ensure that this part of the formula is always valid.
Try this:
IF({Timeline#End}<>"", IF({Completion Date}<>"", IF(DAYS({Timeline#End},{Completion Date})>0, WORKDAYS(LEFT({Timeline#End}&"2000-01-01",10), LEFT({Completion Date}&"2000-01-01",10))-1, IF(DAYS({Completion Date},{Timeline#End})>0, "Complete + days", "Complete 0 Days")), "Simsalabim!"), "-")