Powershell to monitor for SharePoint logs based on correlation ID

Apart from ULS, you can use powershell to search for a correlation and browse it in notepad, example:
Get-SPLogEvent -starttime (get-date).addminutes(-20) | Where -Object {$_.Correlation -eq "5918349c-c5a0-908b-6f2f-f6078c7382e5"} | fl > c:\temp\errors.txt; notepad c:\temp\errors.txt