"Mushroom" Starbase
ST III: The Search for Spock (?)

Ferengi Shuttlepod
I have no idea on this one. Could be TNG's "The Price", but then again...

Klingon K'Vort-Class Bird of Prey
TNG "A Matter of Honor"

Klingon Vor'Cha-Class Attack Cruiser
TNG "Reunion"

Peregrine Fighter (the triangular version used in "The Maquis")
Could be either TNG's "Preemptive Strike" or DS9's "The Maquis", or something else?

Type-6 Shuttlecraft
TNG "The Outcast" (?)

Type-7 Shuttlecraft
TNG "Skin of Evil" (the shuttle that crashed on the planet)

Type-7 Shuttlecraft physical model
(This is the one that is seen powering up the engines before it cuts to a special effects shot. It was shown in TNG's "Unnatural Selection", but that seems a little late somehow...)

Type-15 Shuttlepod
TNG "Time Squared" (again, seems too late in the season for the shuttle to appear, but its the only show that comes to mind)

Yeager-Class
DS9 "In The Cards"

Starbase 375 (where Admiral Ross was stationed)
DS9 "A Time To Stand"

Danube-Class Runabout (with sensor module)
DS9 "Armageddon Game"

Upside-down Sydney-Class transport (seen docking at DS9)
DS9 "Accession"

Bajoran Transport (the orange ship that is docked at DS9 in its opening sequence)
DS9 "The Circle"

Jem'Hadar Bug
DS9 "The Jem'Hadar"

Jem'Hadar Battlecuiser (not the one seen in "Valiant")
I have no idea on this one.

Type-9 Personnel Shuttlecraft (also Class 2)
VOY "Threshold"

And last but not least, the Enterprise wall display in Picard's observation lounge. When was that first seen? I remember seeing the observation lounge in TNG's "Too Short a Season", in which an Admiral overdoses on a youth drug. He talks to Karnas in the lounge, but the room was so dark that I'm not sure if the wall display was installed yet or not.)

If you could help with any of these entries, my lasting gratitude to all of you.

Can't remember TSaS

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"I... love you more... than I did the week before... I discovered Alcohol""
-The Barenaked Ladies

For the Danube-Class with the sensor pod, can you elaborate on the scene with the said runabout? I've watched the episode a long time ago, and I just can't seem to see a pod-equipped runabout in any scene.

As for the Jem'Hadar battlecuiser, were all battlecruisers shown in "In Purgatory's Shadow" the V-type? I remember the scene in which the Jem'Hadar forces poured out of the wormhole, both bugs and battlecruisers. Shouldn't at least one of them be the battlecruiser we see later docked at DS9 in "Ties of Blood and Water"?
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Phase III: Where No One Has Gone Before...
"A man's reach must exceed his grasp, or what's a heaven for?"
Robert Browning, Andrea del Sarto

2) I believe the upside down Sydney was in "Trials and Tribble-ations"

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"The one, the only, THE 359!"

Starbase 359... hmm.

Starbase 375-type was seen in "Blaze of Glory" for the first time, IIRC.