What happened to the third stage with the instrument ring and the loose panels of the LEM Adaptor?
Depends on the mission. For Apollos 8, 10, 11 and 12, the excess LOX on the S-IVB was vented in a forward direction to slow the stage down. This allowed the moon to cross its path before it got there, so it swung around the trailing "edge" of the moon. The moon dragged it along in its orbit, acting as a slingshot to eject it into an earth escape trajectory so that they went into independent orbits around the sun -- where they remain today.
Starting with Apollo 13, the LOX dump events were tuned so that the stages would hit the moon. Not only did this get rid of some space junk (though space junk in solar orbit isn't much of a problem) but it created some nice, well-calibrated seismic signals for the seismometers left on the moon. This helped probe the moon's interior structure.
As Zakalwe points out, Apollo 12's S-IVB was a special case. It was intended to slingshot into solar orbit, but it didn't approach the moon closely enough and remained in a very high earth orbit for a while before perturbations finally ejected it into solar orbit. In the early 2000s, it was temporarily recaptured into a high earth orbit where it was briefly mistaken for a natural asteroid. It then left earth orbit again a few years later.
Northern Lurker is right that what happened to the SLA panels depends on the injection trajectory. For the early missions that used the free-return trajectory, they almost certainly looped around the moon, returned to earth and hit the atmosphere. I'm not sure about the later missions, but they're likely in solar orbit.
One of the more persistent legends among UFO enthusiasts (another fairly crazy group) is that the Apollo 11 crew saw a UFO on their way to the moon. From the discussions with the ground it's quite obvious that they merely saw one of their SLA panels.
