Currently zabbix suports log monitoring. What is lacking, may be great to have and possibly not heavy to implement is actual log monitoring for defined events/regexp occurrence within a period of time.
You have possibility to search and capture of values in the logs defined with regexp. Count of instances found should be also implemented. In that way you can easily monitor occurrence of errors, warnings or items of interest over a time and find out how often they were found in logs over time.
This cut down the need of usage logs post-processing and using extra tools like logstash for basic log health checks making zabbix more feature riched.

Let me know your thoughts over that.