I see that the SR3 rulebook is getting a reprint. I'm wondering, is it being errata'd or will it really be a reprint? and secondly, is there any chance we'll see a hardcover version any time soon?

Most reprints have some amount of errata. It will not be a hardcover; the economics of doing a hardcover reprint 5 1/2 years into a core books lifespan don't make sense.

Will there be a call for errata, or is it a done deal? In particular, will the text for Trid Phantasm be changed from "convincing visual illusion" to "convincing multi-sensory illusion", as per MITS?

The book is already at the printers, I believe.