To prevent receiving and logging many unimportant syslog messages and missing important, you can set the maximum severity level. Messages with a higher severity level (lower priority!!!!) than the level specified, will be ignored.
By default, Monitor one accepts syslog messages matching the severity setting from any host. UNCHECK the Accept Syslog messages from any host checkbox in order to accept only syslog messages from hosts that have been added to the network map!
Every time a syslog message is received that causes an alert, a small green pencil is shown on the map (at the right of the device object that has sent the message) in order to draw attention. How long the small pencil stays visible is determined by how long a syslog alert stays active. (see Options|Global configuration, Alerting tab). Uncheck the checkbox if you do not want the indicator to be visible on the map!