I have numerous D-Link DGS-1500-28 switches with firmware 1.00.013, 1.10.005 and 2.10.002 on it, and there are no visible option to set up date/time via web- or telnet-interface.
Device uses date/time in logs, but there is no idea, where it obtains it from: now it is different days in 2009 for 1.00.013, in 2011 for 1.10.005 and in 2012 for 2.001.006. The date showing is even not 01/01/YYYY + system uptime, as it could seems to be.
This manual for the DGS-1500-20/28/52/28P switches describes setting the time manually or via SNTP on page 49. Perhaps you just need to upgrade the firmware (seeing as how this manual is for firmware version 2.11.