We also know that he had died and been re-embodied. This was a special factor, according to Tolkien. Those of the Eldar who had passed through death came back somewhat stronger.

: Was there anything that Glorfindel couldn't do? (except face
: the Dark Lord himself) Was he capable of the sort of Songs of
: Power that such Noldo as Finrod (striving against Sauron in the
: dungeons of Minas Tirith) and his sister Galadriel (throwning
: down the walls of Dol Guldur) were capable of, or was his just
: a very capable combatant who overcame his foes with a strong
: arm and a keen edged sword.

I think all the Elves used song to express their will. It was the manner of their "making magic", as Sam might put it.

: After he died and returned back to Middle Earth was he anymore
: potent than before? It seems to me that he could not have been.
: In fact I would suggest that he was less potent, for it seems
: that whenever one of the Maia got tanned (Sauron) it took them
: time to recover all their power - did elves returning from the
: Halls of Mandos obey the same rules?...

Just as death of the body was different for the Elves from death of the body for Men, so it was different for them from death of the body for the Ainur.

The Ainur CREATED their bodies -- these were expressions of their will. They could embody or dis-embody themselves at will. The Elves could not do so. If an Ainu was killed, its will was weakened -- the sudden separation of the will from its expression was a severely traumatic event. For creatues like Sauron and Melkor, who had given themselves over to evil and hatred, the result of bodily death seems to have been entry into a period where they were consumed by harsh emotions. Gandalf said that if the One Ring were destroyed Sauron would become "a spirit of malice that gnaws at itself in the shadows, but cannot again grow or take shape."

The crucial point with Sauron's loss of the One Ring is that he lost most of his native strength. He would not be able to recover complete control over himself -- his will would be lost in the malice and anger that overwhelmed him, so he could not focus his thought on taking shape again.

Melkor might be able to return in time because he had diffused most of his native strength throughout Arda itself. Arda was Morgoth's Ring, as Tolkien put it, and just as Sauron's Ring anchored him to the world and provided him with the means to remanifest himself, so Melkor may eventually reover his strength and return in power to Arda.

Other Ainur (such as the Balrog of Moria) would be subject to the same fate as Sauron and Melkor if they were killed. They would be consumed with malice, and unable to reconstitute themselves. If their native strength was insufficient, they would remain in that state until the end of Time. But who knows? Maybe some day Gothmog Lord of Balrogs will reappear -- weaker, perhaps, than before, but still capable of incarnating himself.

:...Was it not the light of the trees that made the Noldor people
: what they were and while bathed in it they grew in power. With
: the trees gone, where could Glorfindel have gotten any more
: power than he possessed before. Is it possible that when the
: Valar gave leave for him to return to Middle earth they somehow
: enhanced him as Gandalf was enhanced when he returned as
: Gandalf the White?

No. The Trees themselves did not really do anything to the Eldar of Aman. Their light was something special, there is no doubt about that. But the Eldar were tutored by the Valar and Maiar for several ages in Aman, and the Valar were able to actually enhance them in mind and in body. All Elves would have benefitted from that special gift had they gone to Aman. It was part of the Valar's purpose in summoning the Elves to provide them with a sustenance that would stave off the world-weariness and fading which would be their fate in the Mortal Lands.

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The Fairy Tales of J.R.R. Tolkien: Roverandom, Farmer Giles, Smith of Wootton Major