what i understand from the web.xml esp for the part of web-app version="3.0"
is the version of your servlet. So, i restrict my answer to the servlet version and why it is so important. As you may know version of your servlet controls most of the other standards when you are programming with Java EE.
For example,
JSF 2.0 requires SERVLET 2.5 comes with JAVA EE5 and WEBLOGIC 10.3.X support all these technologies, for other containers you should check the release notes. Secondly,
JSF 2.1 requires SERVLET 3.0 comes with JAVA EE6 and WEBLOGIC 12c supports all these technologies. Of course backward compatibility is ensured, however most of the cases it's possible to have some problems.
when we check the weblogic 12c release notes, i starred the most important technologies supported along with the servlet version. i hope this is also useful for you with the great answer of Miljen Mikic.
Standard Version
Contexts and Dependency Injection for Java EE 1.0
Dependency Injection for Java EE 1.0
Expression Language (EL) 2.2, 2.1, 2.0
Only JSP 2.0 and greater supports Expression Language 2.x.
JAAS 1.0 Full
JASPIC 1.0
Java API for XML-Based Web Services (JAX-WS) 2.2, 2.1, 2.0
Java API for RESTful Web Services (JAX-RS) 1.1
Java Authorization Contract for Containers (JACC) 1.4
**Java EE 6.0**
Java EE Application Deployment 1.2
Java EE Bean Validation 1.1
Jave EE Common Annotations 1.0
Java EE Connector Architecture 1.6
Java EE EJB 3.1
Java EE Enterprise Web Services 1.3, 1.2, 1.1
Jave EE Interceptors 1.1
**Java EE JDBC 4.0, 3.0**
Java EE JMS 1.1, 1.0.2b
Java EE JNDI 1.2
**Java EE JSF 2.1, 2.0, 1.2, 1.1**
Java EE JSP 2.2, 2.1, 2.0, 1.2, and 1.1
JSP 1.2. and 1.1 include Expression Language (EL), but do not support EL 2.x or greater.
Java EE Managed Beans 1.0
**Java EE Servlet 3.0, 2.5, 2.4, 2.3, and 2.2**
Java RMI 1.0
JavaMail 1.4
JAX-B 2.2, 2.1, 2.0
JAX-P 1.3, 1.2, 1.1
JAX-R 1.0
JAX-RPC 1.1
JCE 1.4
**JDKs 6.0 (aka 1.6), 5.0 (aka 1.5, clients only)**
JMX 1.2, 1.0
JPA 2.0, 1.0
JSR 77: Java EE Management 1.1
JSTL 1.2
Managed Beans 1.0
OTS/JTA OTS 1.2 and JTA 1.1
RMI/IIOP 1.0
SOAP Attachments for Java (SAAJ) 1.3, 1.2
Streaming API for XML (StAX) 1.0
Web Services Metadata for the Java Platform 2.0, 1.1