This blog post explains how to disable the short animation when a new tab is opened in Mozilla Firefox. The solution was tested with Firefox 11 on Linux, but it should work in all versions between 4 and 11, on any operating system.
This question has been asked and answered many times on the web, and most of the answers suggest toggling browser.tabs.animate to false in about:config. However, this disables animation only if there are a few tabs so that horizontal scrolling is not needed. To disable new tab scrolling animation as well, toggle toolkit.scrollbox.smoothScroll to false as well. The change takes effect in windows you open afterwards.