Period correct is my only real sticking point; as for being a replica/bling/functional, that's really down to the individual bike. I've seen good and bad examples of every type.
The only thing I really fail to see the point of is modern, workhorse parts on a retro frame. Fair enough if it's an old frame of yours and you're keeping it going as a commuter or whatever - but why post it on this website?*
*There are exceptions to this, I believe that some modern parts are retro and also that some retro bikes are so timeless that modern parts are suitable (i.e. an RC-300 is still retro, so being built with modern XTR and discs is not an issue for me. Also, some really good Ti frames deserve to be ridden hard and require the componentry to match). But there is a large population here who think retro only means old, therefore this philosophy is perhaps not popular.