There's little problem that I've ever heard playing HD Video on the CoreDuos.http://www.macworld.com/2006/03/firstlooks/minifinal/index.php said:
There's less Success when playing HD with a CoreSolo (which I have hooked up at home) and ArsTechnica has a good breakdown here:
Mac mini (Core Solo): Page 3
EDIT: I just realized that the MacWorld MacMini review I quoted is from April 2006! Wow. 17 months ago. The Mini really is LONG in the tooth -- maybe all those rumours of Apple abandoning it are true.