Is it possible to get security patches for LibreOffice without downloading the entire installation software?
Currently it is not possible to update parts of LibreOffice. LibreOffice is evolving at such a fast pace that any security update is included in the following version (which is released on a nearly monthly basis)
http://wiki.documentfoundation.org/ReleasePlan
So the simple anser is: You do need to download the full installer.
So what would you recommend to users who don’t wish to download a couple of hundred MB each and every month just to stay secure?
And how about having a stable product that can be kept secure without having cutting edge ‘improvements’ that the user may never want to use?
I think there is a plan to have a LTS (Long Term Support) version where only security and fixes are added. In fact people who want a stable release should stick with version 3.4.x. As for partial updates read this Why is "The automatic download of the update...currently not available"?
You don’t have to download a new release every month. While there are bugfix releases, they are not security related. There have only been a total of four security-releases http://www.libreoffice.org/advisories/ so far…
I would suggest that LibreOffice needs an internal updating function that is able to replace any code that needs a security patch efficiently without needing a complete download and installation of the entire package. What, download over 200 MB to change one line of code?
It can be done because Google have done it with their much smaller package, Google Chrome.
It does need that. But it also needs someone who has the time and knowledge to add that (and remember this is a multi-platform Office suite so it would have to work for all OSes) 
Why is editing so painfully slow on the fastest intel 8 core machine with a nvida 2mb graphics card. Is it microsoft or adobe program interfering?
How to prevent this 5 minute delay between each line insertion?
About what security patch?