Has anyone implemented anything custom in Chatter to allow for the "Edit" of a Chatter post on a feed rather just the standard delete function? Just looking for a quick and efficient way to implement that type of functionality without having to delete an entire post because of a misprint.
No, it isn't possible to edit a Chatter post after it has been created. See the FeedItem documentation. Update is not a supported call.
From the idea:
While the ability to edit chatter posts came in Summer '15, it lacks the ability to edit chatter posts with links or files attached to it.
From the Spring `16 release notes: Edit Chatter Posts Containing Files or Links
So you wrote an awesome Chatter post and attached an even more awesome picture, but then you forgot to @mention your boss. Previously, you had to use comments to make any changes to Chatter posts that contained files or links. Now you can simply edit the original post. This feature is available in Salesforce Classic and the Napili template in Salesforce Communities.