Plone 4.3.4.1 is pretty smart. However, I built up my personal Plone site without organizing where I upload the images to, etc. Can I move images and documents to subfolders, etc, and still have images that work and aren't broken? Thanks in advance!
There are several mechanisms that Plone uses to let you do this:
most editors should be configured by defaults so that they really write resolveuid links instead of the path to an image or link target. These are replaced with links only when a page is shipped to a browser, and the IDs do not change on move or rename. (On copy, they will change, because the IDs need to be unique.)
in case you ever manage to get a resolveuid past the output filter, the links are actually calleable and will redirect to the current location.
if you move/rename something and there is an external link to the old location, the error page mechanism comes into play: it tracks, broadly speaking, all past names and locations of your page or image (until a new page/image at such a location comes into existence) and will redirect there.
So, broadly speaking, you should be fine. If in doubt (I've seen plenty of cases where output filters mysteriously stopped working all of a sudden), you could always try with one image first and observe the result.