If you insert measures at the front, anything following that will get shifted forward. If you lock the number of measures in a system, you can insert measures into that system, and not affect what follows. That system, of course, will need reformatting.

Things like this are best prevented by saving the final formatting for the last step.

Hi Mike, thanks for the reply.  Unfortunately, I do not have the luxury of saving the final formatting until the last step because the pieces are for musical theatre where rewrites/changes are continuously being made, measures cut, measures inserted, etc. until the show is finally "gelled". 

I do have the number of measures locked in the existing systems. However, I'm a little unclear regarding your reply: "If you lock the number of measures in a system, you can insert measures into that system, and not affect what follows. That system, of course, will need reformatting."  What system will need reformatting?  The existing systems whose number of measures I have already locked?  Please advise.

The system onto which you have inserted the new measure.

… when I try to insert measures at the beginning of the piece, my existing measures get moved to the next page and empty staves that I had previously hidden, suddenly become visible again and it messes up the entire format of the piece and so I have to go back and painstakingly readjust each individual stave/system (including all of the texts I have attached to measures!) back to how they were before I inserted the measures into the piece!  Is there a way to insert measures in Finale and keep this from happening? …

Do not insert measure stacks.

Instead, use the Page Layout Tool to insert staff systems.

In that way all the following systems will retain their formatting.

I've never inserted staff systems using the Page Layout Tool before, Peter.  Thanks, I'll give that a shot!