SQL Server error log monitoring In SQL server instance(s) I manage; I see a lot of activity and messages in SQL server error log for e.g. backup or transaction log backup completed etc.. We have quite a few databases in one instance and amount of error log messages is sometimes quite a few to dig into. 

As an accidental DBA, What approach or script can I use to filter the error log for date range specified or finding or filtering troubling errors out of lots of informational messags?

I meant to ask, is there is a T-SQL script or DMVs you can use to filter the error log?
I suggest that you circumvent reading the error log directly and instead implement SQL Agent Alerting.  Under this methodology, you'd simply create alerts for, say, when SQL Server throws an error (I recommend separate alerts for severity levels 19 -25) and tell SQL Server to email you when the error occurs.  

You can then generally ignore error log except for specific troubleshooting situations.

General details are here. The details for setting up SQL Agent alerts specifically using SSMS are on TechNet are here and are the same in Books On-Line here.

Hope this helps,
-Kevin

@kekline