I have several thousand tags currently and want to completely re-do all my post tags. As a result, a lot of the current ones won't be used again. Before I insert the new tags, I want to delete all the current ones from the tag admin panel. Will doing so cause any SEO or Google Webmaster issues? I don't want Google coming along and saying "I can't find 500 of your index tags...PageRank-2."
PageRank is per page, not per site and only reflects the link popularity of a page, nothing more. So removing those pages won't directly affect the PageRank of your remaining pages. It will indirectly affect their PageRank as every page inherenty has PageRank and by removing those pages you will not be "passing" PageRank from them to your other pages. But that will be offset by your new tag pages so this really is a non-issue.
Also, pages are removed from the Internet all of the time. Just expect Google to report lots of 404 errors in your account once those pages are deleted.
Well tag pages in WordPress for example are usually indexed. I'm not sure what application you are running but I would check to see if those tag pages are indexed. Go into your analytics and see what the top landing pages are from organic searches and search for the word tag or tags to see if any of your tag pages are ranking high for some keywords.
The tag pages may also be helping with internal relevant links. Depending on how unique, and how much content you have the tag pages being mostly relevant for that tag linking to posts could possibly be helping rank the post pages.
I would first see where the tag pages are ranking as well as other pages on my site, from there i would determine which tags to keep and which to get rid of