[Boromir88]

After Gandalf died and was sent back by Eru, he was granted more power and authority. For Eru knew now that only Gandalf would be the one to stay true to his task and someone needed to deal with Saruman. Tolkien clearly points this out in Letter 156:

That I should say is what the Authority wished, as a set-off to Saruman. The 'wizards', as such, had failed; or if you like: the crisis had become too grave and needed an enhancement of power. So Gandalf sacrificed himself, was accepted, and enhanced, and returned. [...]He was sent by a mere prudent plan of the angelic Valar or governors; but Authority had taken up this plan and enlarged it, at the moment of its failure.

The Valar sent the Istari as a plan in order to help the free people's combat Sauron. After the other Istari failed and Gandalf was the only one who would stay true to the task, the Authority (Eru) got involved and made Gandalf more capable of being able to complete the task.

So, what kind of "authority" did the Istari have, if any? What exactly was their task? Who perhaps knew about them? I think these quotes will answer it to the best that we can:

When maybe a thousand years had passed, and the first shadow had fallen on Greenwood the Greatm the Istari or Wizards appeared in Middle-earth. It was afterwards said that they came out of the Far West and were messengers sent to contest the power of Sauron, and to unite all those who had the will to resist him; but they were forbidden to match his power with power, or to see to dominate Elves or Men by force and fear.~Appendix B: The Third Age

So, the people of Middle-earth see these old men, and they see them as "messengers" sent to contest Sauron. I think this quote also backs up the authority that the Istari could command. Now they can't dominate over anyone, and they can't force anything. But, it was their mission to unite those who would combat Sauron, which implies they would have an authoritative sort of role. They themselves would not be able to lead directly against Sauron, or challenge him. However, if they wanted to complete their task they would have to take up an authoritative role, in order to unite the Free Peoples against Sauron.

Let's look at Theoden who accepts Gandalf as his "new counselor" after Grima, I would say a "counselor" is a title that holds certain authorities:

"Nonetheless I miss now both my counsellors, the old and the new. But in this need we have no better choice than to go on, as Gandalf said, to Helm's Deep, whether Erkenbrand be there or no..."~Helm's Deep

And this is how Gandalf often acted, as a guide, counselor, advisor. He couldn't dominate and force anyone against their will, as that would go against his "task." But he could instruct and guide, and "Counselors" have authoritative power. Eventhough if they aren't the one's to make the decisions, they can influence and in Theoden's case he takes Gandalf's advice. With Denethor, he doesn't, and Gandalf is forbidden to force Denethor against his will.

For sure, Cirdan certainly knew who Gandalf really was:

For Cirdan saw further and deeper than any other in Middle-earth, and he welcomed Mithrandir at the Grey Havens, knowing whence he came and whither he would return.
"Take this ring, Master," he said, "for your labours will be heavy, but it will support you in the weariness that you have taken upon yourself. For this is the Ring of Fire, and with it you may rekindle the hearts in a world that grows chill..."~Appendix B: The Third Age

Also, notice Cirdan called Gandalf "master," displaying more authority that the Istari had.

I agree with narfforc, whether Gandalf referred to himself as steward once or thousands of times. He called himself a steward, and even further explained what his job was. And those who knew who the Istari were accepted their authority (as shown with Cirdan). As well as in Theoden's case who takes Gandalf as his counselor (even though if Theoden probably didn't know of Gandalf coming over from the West as messengers).

And with Faramir:

"Gandalf!" said Frodo. "I thought it was he. Gandalf the Grey, dearest of counsellors. Leader of our Company. He was lost in Moria."
"Mithrandir was lost!" said Faramir. "An evil fate seems to have pursued the fellowship. It is hard indeed to believe that one of so great wisdom and of power - for many wonderful things he did among us - could perish and so much lore be taken from the world..."~The Window on the West

We seem to have several people around Middle-earth who have accepted Gandalf. Whether if it was like Cirdan who actually knew who he was and why he was there, or Theoden, Faramir, Aragorn, and many others who accepted his counsel and leadership, but didn't know.

The other istari abandoned their tasks, or turned away. But, in Gandalf's case he was well known in Middle-earth, and known by many names, and known for many deeds. Which, I think shows he commanded a certain authority when he was around as those willing saw him as a friend and took his advice.

I hope this isn't too hard to follow, I jumped around a lot, I think and just jumbled everything.