What is the difference between a panelbox that will allow tandem breakers and one that won't? If the panel is old and missing the CTL label is it possible that tandem breakers are still OK? Does the number of neutral wire conncections on the neutral bar mean anything? i.e. there are a lot more holes that spaces for single breakers. Of course some are for different size wires.

The total load on the panel can't increase past the main breaker ampacity of course.