PHPJunkyard support forum

My setup of Hesk is set to only email on ticket update by staff but when a client responds to any ticket or if an admin changes the priority or category of a ticket a notice will appear at the top stating "Note: Could not send email notifications. Please notify webmaster at %EMAIL%".

Is this a bug or by design? I get at least a few customers a week alerting me of the notice.

It's not by design, the notice will be displayed whenever Hesk tries to send an email but fails to do so.

Hard to say what is going on without seeing it in action (both the help desk and the set up), but first thing you should do is get familiar with when and to whom Hesk sends emails:
https://www.hesk.com/knowledgebase/?article=94

That should give you an idea where emails are sent. Then make sure that:
1. sending emails work
2. all staff have either a valid email or email notifications disabled

P.s.: turning on Debug mode in Admin > Settings > Help desk then repeating the action should give you a more verbose error message.

Debug mode should then be turned off for normal operations.