I have Tomcat 4.1.36 in my development environment and Tomcat 4.1.27 in the server. Will there be a problem if I put a War file created from my 4.1.36 local environment onto a Production 4.1.27 environment?
Generally, no. There is a small chance that you might run into a bug that has been fixed between .27 and .36, but as long as the web app adheres to the standard servlet/JSP stuff (meaning it doesn't muck with Tomcat internals) you should be fine. Changing digits after the second decimal point indicate bug fixes only, no new functionality.