You need media server software working on your nas.
1. Media has to be in format ps3 actually understands, so no .iso, .mkv, .ape, .flac, .shn and .ogg files. Transcoding is not something DNS-323 is cut out for.
2. Movies with dts sound must be tinkered with (mostly).
3. Sometimes you have to mess around with filename extensions to get streaming to work (.mp4 -> .mpg or .mpeg, sometimes the other way round).
4. Sometimes files which should be supported (some .wmv, .avi and divx) do not play.
5. If you use wired connection, better use gigabit, not fastethernet. 1080p movies streamed well over wifi, not-so-good over fastethernet (100 Mb/s), perfect over gigabit ethernet. Maybe it is resolved with newer ps3 fw, can't say. Seemed like buffering issue.
6. You are better off with twonky than with built-in upnp server (which is some castrated form of mediatomb clone knockoff). Your media database actually updates itself and does it quickly. Older versions (5.*) even allowed media playback after trial period expired (through ps3 net browser interface). I don't know about 6.*, I successfully wrestled my cheapness and bought it.
7. I believe the router has nothing to do with it, as both devices (DNS-323 and ps3) are on local network.