diff --git a/posthog/api/alert.py b/posthog/api/alert.py
index a177c61b0322d..3275ae53d7933 100644
--- a/posthog/api/alert.py
+++ b/posthog/api/alert.py
@@ -215,6 +215,14 @@ def update(self, instance, validated_data):
             # If anything changed we set to NOT_FIRING, so it's firing and notifying with the new settings
             instance.state = AlertState.NOT_FIRING
 
+        calculation_interval_changed = (
+            "calculation_interval" in validated_data
+            and validated_data["calculation_interval"] != self.calculation_interval
+        )
+        if conditions_or_threshold_changed or calculation_interval_changed:
+            # calculate alert right now, don't wait until preset time
+            self.next_check_at = None
+
         return super().update(instance, validated_data)
 
     def validate_snoozed_until(self, value):
diff --git a/posthog/tasks/alerts/checks.py b/posthog/tasks/alerts/checks.py
index d6f8c020f1d7e..539c66bf348ad 100644
--- a/posthog/tasks/alerts/checks.py
+++ b/posthog/tasks/alerts/checks.py
@@ -11,7 +11,7 @@
 from django.conf import settings
 from django.db import transaction
 import structlog
-from sentry_sdk import capture_exception
+from sentry_sdk import capture_exception, set_tag
 
 from posthog.errors import CHQueryErrorTooManySimultaneousQueries
 from posthog.hogql_queries.legacy_compatibility.flagged_conversion_manager import (
@@ -289,10 +289,10 @@ def check_alert_and_notify_atomically(alert: AlertConfiguration) -> None:
         error_message = f"AlertCheckError: error sending notifications for alert_id = {alert.id}"
         logger.exception(error_message)
 
-        capture_exception(
-            Exception(error_message),
-            {"alert_id": alert.id, "message": str(err)},
-        )
+        set_tag("alert_config_id", alert.id)
+        set_tag("evaluation_error_message", str(err))
+
+        capture_exception(Exception(error_message))
 
         # don't want alert state to be updated (so that it's retried as next_check_at won't be updated)
         # so we raise again as @transaction.atomic decorator won't commit db updates
diff --git a/posthog/tasks/alerts/utils.py b/posthog/tasks/alerts/utils.py
index 06b94cc938089..0084cc6efa0e4 100644
--- a/posthog/tasks/alerts/utils.py
+++ b/posthog/tasks/alerts/utils.py
@@ -59,8 +59,8 @@ def alert_calculation_interval_to_relativedelta(alert_calculation_interval: Aler
 def send_notifications_for_breaches(alert: AlertConfiguration, breaches: list[str]) -> None:
     subject = f"PostHog alert {alert.name} is firing"
     campaign_key = f"alert-firing-notification-{alert.id}-{timezone.now().timestamp()}"
-    insight_url = f"/project/{alert.team.pk}/insights/{alert.insight.short_id}?alert_id={alert.id}"
-    alert_url = f"{insight_url}/alerts/{alert.id}"
+    insight_url = f"/project/{alert.team.pk}/insights/{alert.insight.short_id}"
+    alert_url = f"{insight_url}?alert_id={alert.id}"
     message = EmailMessage(
         campaign_key=campaign_key,
         subject=subject,
@@ -86,14 +86,14 @@ def send_notifications_for_breaches(alert: AlertConfiguration, breaches: list[st
 def send_notifications_for_errors(alert: AlertConfiguration, error: dict) -> None:
     subject = f"PostHog alert {alert.name} check failed to evaluate"
     campaign_key = f"alert-firing-notification-{alert.id}-{timezone.now().timestamp()}"
-    insight_url = f"/project/{alert.team.pk}/insights/{alert.insight.short_id}?alert_id={alert.id}"
-    alert_url = f"{insight_url}/alerts/{alert.id}"
+    insight_url = f"/project/{alert.team.pk}/insights/{alert.insight.short_id}"
+    alert_url = f"{insight_url}?alert_id={alert.id}"
     message = EmailMessage(
         campaign_key=campaign_key,
         subject=subject,
-        template_name="alert_check_firing",
+        template_name="alert_check_failed_to_evaluate",
         template_context={
-            "match_descriptions": error,
+            "alert_error": error,
             "insight_url": insight_url,
             "insight_name": alert.insight.name,
             "alert_url": alert_url,
diff --git a/posthog/templates/alert_check_failed_to_evaluate.html b/posthog/templates/alert_check_failed_to_evaluate.html
new file mode 100644
index 0000000000000..4cf8a5f5d54e0
--- /dev/null
+++ b/posthog/templates/alert_check_failed_to_evaluate.html
@@ -0,0 +1,10 @@
+{% extends "email/base.html" %} {% load posthog_assets %} {% block section %}
+    <p>
+        The <a href="{% absolute_uri alert_url %}">{{ alert_name }}</a> alert failed to evaluate for insight <a
+            href="{% absolute_uri insight_url %}">{{ insight_name }}</> with the following error:
+    </p>
+    <p><i>{{ alert_error }}</i></p>
+    <div class="mb mt text-center">
+        <a class="button" href="{% absolute_uri alert_url %}">Manage alert</a>
+    </div>
+{% endblock %}{% load posthog_filters %}