Quick list of HTML and Javascript properties & standards that are supported in PIE in Windows Mobile 2003 SE (more specifically Pocket PC). The browser itself is a bit outdated nowadays, but seems to be readily available in "industrial-strength" devices.

Method / Function	Works (Yes/No)	Notes
document.all	No	HTML elements can only be accessed through dot-notation, so only first level elements under a body tag of a DOM tree can be modified. Exceptions: Form fields can be accessed through form.elements -collection.
element.innerHTML	Yes	-
XHR (Ajax)	Yes	new ActiveXObject("Microsoft.XMLHTTP")
HTTPS (SSL)	Yes	Seems to support 128-bit and also unsigned certs
onClick-event	Varies	Seems to be supported on at least anchors ( A-tag) and images. No support for onClick on DIVs.
element.focus()	Yes	-
onLoad-event	Yes	e.g. <script for="window" event="onload">     ... code ... </script>
onkeypress onkeyup onkeydown -events	No	See onChange-event
onChange -event	Yes	The browser triggers an onChange-event when a form element loses focus ( Enter/Return is pressed, for example)

Links:

HTML Reference for Pocket Internet Explorer (microsoft.com)