Whenever I boot up Minecraft, and go on any world, adventure map, minigame, etc. on singleplayer, I get horrible lag that is serverside. I can tell, because this does not occur on servers. It has a delay of about 5 seconds. I have tried opening to LAN, and things like hosting a server and connecting to localhost. I have tried hosting a server and having friends join it, and they get the same lag, but only on my server. I tried giving Minecraft/ the server 8GB of RAM, which did not help much. Things like plants and tall grass break instantly and without lag, But blocks and animals are 5 seconds behind. Here is footage of the supposed bug: https://www.youtube.com/watch?v=jqTY72_0Usc
Please do not mark unreleased versions (anything starting with "Future Version") as affected. You don't have access to them yet.
Try updating your Java to the most recent version (1.7.0_51) and using the default settings (i.e. 1gb of memory) and pure vanilla setup (no resource packs, etc.).