Observations in TNG: "When the Bough Breaks"

Aldea will appear again as Vagra II in "Skin of Evil".
Re-Used Planets in TNG

There is a characteristic latticework in this window on Aldea.

Mike Okuda: "The geodesic latticework in the window of the First Unit chamber on Aldea was actually a children's playset that Herman [Zimmerman] had purchased for this set. It was a brilliant way to get us a bit of production value that he probably wouldn't have had the time or the money for otherwise. Later, Herman recycled the same dome on the roof of one of the buildings in Paradise City in Star Trek: The Final Frontier."

The same graphic appeared in "The Last Outpost", where it depicted Delphi Ardu IV, in "Too Short a Season", where it depicted Persephone V, and in the previous episode "Home Soil", where it was used to represent Velara III.
Re-Used Graphics

The Custodian console reappeared in "Star Trek V: The Final Frontier" as a Klingon communications console on Nimbus III.
Consoles Built for Star Trek

The Aldean logo, which appears on several walls and tapestries in this episode, is seen behind Wesley.

Mike Okuda: "I'm pretty sure that Cari Thomas designed the Aldean logo for me. I cut up the 'petals' of the flower, and made them into the Aldean alphabet."

The Aldean communicator was re-used at least twice, many years later in two Voyager episodes. It appeared as a device used to measure the polaric radiation in "Time and Again" and is seen again in "Prototype" as a Pralor device.
Re-Used Props - Mobile Computers

Stone seats like this appeared in some earlier season 1 episodes, like "Encounter at Farpoint" (in the Farpoint Station mall) and "Code of Honor" (in Lutan's Centerplace).
Re-Used Props - Furniture

Benches like this were also seen on Rubicun III in "Justice" and on the eponymous planet in "Angel One".
Re-Used Props - Furniture

The metallic sculpture seen behind Accolan was also seen on Rubicun III in "Justice". It will be seen again in many later episodes, like "The Outrageous Okona", "The Schizoid Man" and "The Measure of a Man".
Re-Used Props - Decoration

A nice look at the power plant below the planet's surface, which is somewhat reminiscent of the Krell power plant in "Forbidden Planet" or the core of the Death Star.

Both the outer structure of the power plant as well as the central glowing column feature a pattern of repeating hexagons. This pattern will later appear on the walls of the interrogation room aboard the USS Enterprise-D in "The Defector" and "The Drumhead" and also adorn the backwall of the Klingon transporter room aboard Klaa's Bird of Prey in "Star Trek V: The Final Frontier".

Mike Okuda: "I built the Aldean reactor core. Rob Legato and Gary Hutzel came to me and asked me to work with them on that shot. They needed something cool and powerful looking, but had no money in the budget to build anything. I had an idea for an internally-lit structure that would be seen mostly in silhouette. The advantage of this would be that the model could be fairly simple, but would look dramatic because of lighting. I used parts from several children's toys and model kits, including a Space Shuttle launch tower. I think I even used some left-over pieces from the Star Trek: TMP space dock model in the base. Rick Sternbach helped out with some of the scaffolding around the core. The core of the model was a clear acrylic tube with a florescent tube in it. Wrapped around the tube was a sheet of high-contrast black and white film with a pattern that I designed for this. The design incorporated lots of vertical lines and a series of hexagons, which was one of the signature graphic elements that I had used for this planet. Later, I used the same art for the back wall of the Klingon transporter room and the back wall of a Starfleet interrogation room. Rob and Gary loved the model and made it look like this huge, mysterious, powerful reactor."