Symptoms

One specific user has not received escalation email from K2 but other users received it. Is there any method to figure out if an email was triggered from K2 but not delivered or if an email was not triggered at all?
 

Diagnoses

Escalation emails work the same way as e-mail events in terms of sending messages. It means that they use the mail server configured in the string table to send an email. But in addition to this there is an extra step of creating related entry in Escalations table in K2 DB and processing it later.
Any obvious errors/failures are being logged in K2 with default logging level (things like failed escalation triggering or missing/wrong email or issues with SMTP server). Successful actions being logged only with full/debug logging.
In current version of K2 there is no easy way to check/track successful sending of email on K2 side. There is an existing feature request to improve this in the future:

TFS 672985 Ability to store or log mail in an audit table

Also you have to keep in mind that successful sent operation on K2 does not exclude some further issues on Exchange/SMTP side which you have to monitor/check separately.
 

Resolution

At the moment only major errors are logged with default logging level, and successful operations logged only with Debug logging level. In certain cases it may be difficult to locate specific error/success log entry corresponding to sent escalation email.