Currently, there is no way to un-acknowledge a problem which was previously acknowledged (by mistake or not) other than editing the DB in multiple location.
In 4.0.5 (the version i'm using) we're talking about :
https://zabbix.org/wiki/Docs/DB_schema/4.0/acknowledges
https://zabbix.org/wiki/Docs/DB_schema/4.0/events
https://zabbix.org/wiki/Docs/DB_schema/4.0/problem

Would have been nice to be able to un-ticked an ack. problems via the front-end directly.