It would be nice if there is a way to see current server time on "tasks", "last time connected" and other pages that display time in one of the records.

What do you mean by "servertime" the current time in UTC of the server or server-local time? At the moment time is shown in UTC everywhere and must be converted to the viewers local time bythe viewer itself. A nive new feature would be to display the time already converted to the viewers timezone. This would mean to introduce a setting for this and also look into the browser settings and changing all places where time is displayed to this new conversion function.

Actually, there would be some merit in displaying the server's local time, whether in UTC or converted to the viewer's local time.

Most experienced server admins will instinctively install and configure NTP synchronisation tools on their servers, but on smaller 'one man' (or one woman) projects that may get overlooked: I reckon that the NumberFields@Home server is currently running about five and a half minutes ahead of UTC (estimated by a discrepancy between deadlines and the local arrival time of tasks). I've seen it rise to about 20 minutes, before being reset by a reboot. That's just mildly amusing, and causes no immediate harm to anyone: but more seriously, if a server happened to have its clock reset while tasks were in progress, clients with accurate clocks might miss deadlines. Having time visible would allow users to alert project staff to problems more easily.

And even more amusingly, BOINC is designed to cope properly when even the most experienced sysadmin occasionally forgets (as they do) to configure NTP on a new server. For a while, one very famous multi-server project was displaying message board posts as having been made up to a minute in the future, because of a time discrepancy between their BOINC and web servers...