"Is there a way to obtain a permanent pop-up or a red coloured target Icon that could indicate the service failure without pointing with the mouse on it?"
I suppose you could, if you are a programmer, since the source code if freely available. But why? I have over 1000 hosts/services. Can you imagine how many pop ups I would have if the cable fell out of the nic card on my nagios box? It would render that link useless. But, since my box has a hosts.cfg file with decent parent/child hosts defined, if eth0 on my nagios box fails, then the rest of hosts will be "unreachable". It would take me a long time looking at the 1000's of services that are in the "unreachable" state" in the service problems link to find the problem. But looking at the status map, I would immediately see, that the Nagios box is running, but the host "eth0" is down. All the rest are marked "unreachable".
The status map, I think is a misleading name, and should be called "Our Network" or something like that. Your status map should look identical to the layout of your network, i.e. switch A connects B which connects to routerC and host A is on switch, etc. and that is all it should be used for.
You don't want people lingering on your statusmap.cgi file, since it takes alot of resources to generate that page over and over again, depending on how often your page refresh is set in the cgi.cfg file.
So, look at that status map, when you need to see how hostA is connected to the network and is dependant upon having SwitchB up. If switchB is broken, then that is why your HostA is showing "unreachable" and switchB is showing "Down" in the "service problems" link.
Other than that, if you are really interested in knowing what is up/down, you should be looking at the "Service Problems" link.
If it's blank, then life is good. Takes very little resources from apache too.