Have you updated Safari recently?
On Mac systems, the web viewer uses a Safari "web kit" to do its thing so a Safari update could affect the web viewer.
Most up to date version of FileMaker 10 is 10.03. There's a free updater you can use to update to that release.
Updated safari just now and FMP to 10.0.3. Problem still persists. I also tried on another local machine with Firefox....no joy.
I tried running with OSXserver firewall switched off, and then the web sevice switched off. It feels like an application problem. Would chucking the preferences be a safe an logical thing to try?
Trashing Preferences is a very old and simple fix worth trying on Mac systems. You can drag the preferences file out on the desktop and then you can replace it if you find that this is not the issue and want to keep all your settings.