So the status of all hosts and all services is "UP" but yet, you have different totals for the "all problems" If so, what hosts/services are in a problem state? Need more details please.
"I have 10 hosts and one service check for each host. In the "all types" field of the "host status" display it shows 10 for hosts and 10 for services. All hosts are in the UP state and show "0" in the "all problems" field. There is one service in the down state and shows a "1" in the "all problems" field. Now this would be strange, since the service check is check_ping and the host check is "check_fping".
If that is the case, then there might be a service check that is failing for some reason.