After the defeat of Sauron, Elrond, Cirdan and Isildur went to Mount Doom. Elrond encouraged Isildur to destroy the ring. Isildur, however rejected Elrond's bidding.
Now did Gandalf know that Elrond didn't stop Isildur?
If so, why didn't he (Gandalf) blame Elrond.
As is extensively covered in this answer, Elrond and Cirdan had a reason not to take the Ring by force as it would have ensnared them, like it had Isildur, Gollum and Boromir. It is unlikely they would've had enough power to shake of the will of the One Ring.
So regardless of the answer below even if Gandalf had known, he would've known he could not blame Elrond for Elrond had done all he could do without corrupting himself and risking more damage.
This is also a good analysis (although without any quotes) of the nature of the One Ring at the time.
The fall of Sauron led to the ending of the Second Age and the Start of the Third Age. In the year T.A. 2 Isildur and his three sons are slain. 998 years later in T.A. 1000 the Istari come into Middle-earth.
2 Isildur plants a seedling of the White Tree in Minas Anor. He delivers the South-kingdom to Meneldil. Disaster of the Gladden Fields; Isildur and his three elder sons are slain.
Return of the King - Appendix B: Tale of Years
They first appeared in Middle-earth about the year 1000 of the Third Age
Unfinished Tales: The Istari
In these 1000 years the One Ring had been lost, no one had ever seen it again. It was not for another ~1200 years that the One Ring had been found by Deagol and stolen by Smeagol. In this time it is not 100% clear whether Elrond had discussed the ending of the War of the Last Alliance with Gandalf or not. But as stated above, this doesn't matter, as there was no reason to blame Elrond.
From the perspective of the Movies, we can assume Gandalf had not known. Elrond says the following to Gandalf suggesting that he hadn't told him before, speaking as if Gandalf hadn't known before.
GANDALF: It is in Men that we must place our hope.
ELROND: Men? Men are weak. The race of Men is failing. The blood of Numenor is all but spent, its pride and dignity forgotten. It is because of men the Ring survives.
FLASH INSERT: With the broken sword, Isildur slices off Sauron's finger. Elrond reacts.
ELROND (V.O.) (CONT'D): I was there, Gandalf...I was there three thousand years ago when Isildur took the ring.
FLASH INSERT: ISILDUR PICKS UP THE RING AND STARES AT IT, ENTRANCED.
ELROND: I was there the day the strength of Men failed.
ELROND: Isildur...hurry...follow me!
IMAGES: ELROND leads Isildur into the steaming volcano.
ELROND (V.O.) (CONT'D): I let Isildur into the heart of Mount Doom, where the ring was forged: the one place it could be destroyed.
FLASH INSERT: ELROND AND ISILDUR STAND BEFORE THE FIRES OF MT. DOOM.
ELROND: Cast it into the fire...destroy it!
CLOSE ON: ISILDUR...CAPTIVATED BY THE RING.
ISILDUR: No.
The clip can be seen below
Presumably. The Istari (of which Gandalf or "Olorin" was one) were sent AFTER Sauron's initial defeat. The Istari (Wizards) were sent to Middle Earth because the Valar knew that Sauron had not been defeated utterly.
Given Gandalf's relationship with both Galadriel AND Elrond, it can be assumed that he knew their stories intimately. He would have known Elrond was there when Isildur failed to destroy the ring. He obviously knew (or at least found out) the ring was missing, but that it had not been destroyed. Even Saruman admitted the ring had been "[Lost to the sea]".
So, in my estimation the answer is yes, he knew. But Elrond wasn't the bad guy in this situation and the Istari were not sent for revenge, they were sent to be actors on behalf of their associated Valar. They were simply sent to help. And, aside from Saruman (arguably) they did just that.
