As mentioned, no, anything you'd need is already in the 1st edition, you have no reason to buy a newer one (it's not like books about a rapidly evolving technology), however
I've been really wanting to become better in algorithms to further develop my programming and general problem solving capabilities. Thanks!
I'd really advise against using CLR for the task you are setting. I know this is a personal opinion, but I feel like CLR is more of a reference textbook, to be used with caution and a prior indication of what you are looking for, then an all purpose algorithmic textbook. There are many other choices, I'm not sure which to recommend, but perhaps Algorithms by Dagupta, Papadimitriou, et al. would suit you, as it delves rather more into algorithmic paradigms (how to solve a problem using one of three/four algorithm "templates") then with the cogs of specific algorithms---yes, this is a discussion that is also featured as a part of CLR, but in my opinion, with much less tact and pedagogy.
Besides with that last book, money, or which edition to buy shouldn't be an issue as the book is... freely available. (Thank you authors.)