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I don't have experience but 720p, maybe, 1080p, seriously doubt it

It's single core, that's why, if it was Core Duo, then it should be able to
 
Agreed. The 1.83ghz core2duo and upwards have no trouble with 1080p. 720p should be fine, though, on the 1.6 coresolo.
 
will the intel Solo Mac Mini 1.6 GHz do 1080p and 780p playback from Plex?

There was no 1.6 gHz Core Solo. There were 1.5 gHz Core Solo and 1.66 gHz Core Duo, the latter of which can play most HD just fine, largely dependent upon bit rate, audio track and software used for playback.
 
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