Answer by Graham Dunnett

There are security restrictions imposed when running in a webplayer, so, for example, you cannot use System.IO to access the hard drive, and you cannot access remote websites without permission. A long list of Mono classes is shown here: http://docs.unity3d.com/Documentation/ScriptReference/MonoCompatibility.html and the security sand box is here: http://docs.unity3d.com/Documentation/Manual/SecuritySandbox.html