Extensive chatting with various people "in the know" has brought the following information to light:
A lot of the sets used in the first movie were originally built for the aborted
Phase II series, and continued to be used throughout the movie run. However, as a cost-saving measure, sets like the corridors and Captain Kirk's quarters were redressed and recycled for use in TNG (Kirk's quarters in VI were rebuilt; the set had been altered too much to re-use. I believe it became the "junior officers' quarters"). That's why we don't see much of sickbay after
The Wrath of Khan except for a couple of shots in Trek V and VI (and even then, the one in VI is very dark). Certainly the beds used in TNG were taken from the movie set and refurbished; although there doesn't appear to be any statement my The Powers That Be (I'll check some more, though!), the sickbay set appears to have been recycled wholesale. The best thing to do is compare the deckplans for the E-refit sickbay (in "Mr Scott's Guide to the Enterprise") and any floorplan of the TNG sickbay you can find.
The E-D sickbay may have been a new set (and is probably more visible in Trek V than VI - I don't recall) but since another cost-cutting measure invovled matching the lighting set-up from the movies for the TNG sets, it's quite likely it just got a new coat of paint.
However, all sets on Voyager were newly-built (at most, all Voyager will have been able to use, due to differences in layout, would be one or two heavily modified walls). The Voyager sickbay has doubled as the Enterprise-E sickbay, though.
They have done something similar with bridge sets over the years - I'll see if I can assemble something on this in the not too distant future.
Oh, and I forgot. There are plenty of good resources in the Star Trek Files magazine (or in the US, Star Trek: The Magazine - I'd kill to see a lot of the production stuff, since we don't get that

). You might also want to try asking on the Ask Rick Sternbach newsgroup - if I knew where it was I would post there too, since I've got a few questions

If anyone knows, Rick will.
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Top 20 Things You'll Never Hear Said At A Star Trek Convention
#7: "Jim Beam me up, Scotty"
[This message has been edited by JimBeam (edited 13 January 2001).]