Gyus!

Template "Template JMX Tomcat", that shipped with zabbix have no escape of " in the names of Mbeans.
This leads taht most part of items in template are not-supported. Unfortunately, due to the problem I spent several hours investigating this trivial issue. I'm sure many other people too.

E.g:

Instead of 
jmx["Catalina:type=GlobalRequestProcessor,name=http-8080",bytesReceived]

you should use:
jmx["Catalina:type=GlobalRequestProcessor,name=\"http-bio-8080\"",bytesReceived]

This link helped me:
https://www.zabbix.com/forum/showthread.php?t=36714
And you could consider using this template:
https://gist.github.com/hgomez/32091...x-template-xml
It works like a charm for me after setting the values of macroses in templates:
{$AJP_PORT} 8009
{$CONNECTOR_MODE} bio
{$HTTPS_PORT} 8443
{$HTTP_PORT} 8080

Could you please fix default tomcat template?