Implications of changing your post title

I did a search on this topic, but came up with over 2,000 results, so please bear with me when I ask this again.

Some of my earlier posts (from 2 years ago when I was a real newbie) are cryptic and you really can’t tell what the post (actually a podcast episode) is about from the title. I’d like to “freshen-up” some of those old titles. I just want to make sure I understand the ramifications of doing this. What will this do? Am I right that if someone placed a hard link from their website to one of my posts and then I change the post title, their link will be dead?

Other things I haven’t thought of before I go changing the tiles of my posts?

Thanks for the help,

Michael