Is there a source to assert that the leaders of the Jewish people at any given time are always correct in how they lead (perhaps because their decisions are divinely inspired), or is it possible to say that any leader of the Jewish people is no more infallible than a regular person? Is there a middle ground?
The dictionary translates fallible as capable of making a mistake. Everyone is capable of making a mistake. From Moshe Rabeinu hitting the rock, to the Shevatim selling Yosef, etc., there are many recorded instances where Gedolei Yisroel were fallible. However they do have a divine special protection (story of Rabbi Moshe Feinstein Zatzal with Aguna and many others).
I'm going to give you an answer to that question as I heard it from Zalman Posner, Rabbi Emeritus of Congregation Sherith Israel of Nashville, Tennessee. He said:
Before the war in a train station in Europe, several chasidim found themselves waiting for their trains. They decided to use the moment to tell stories of the miracles their rebbes had performed. The fellow from Satmar told his stories, as did the fellow from Belz, and the fellow from Bobov. Finally they got to the chasid from Lvov and asked him to tell stories about his rebbe's miracles.
"I can't think of any," he replied.
"Surely you're holding out," they cried. And they nudged and nudged and finally, he admitted, there was one miracle . . .
"I heard of a business deal in Warsaw that sounded good," he related. "But before I would do a business deal, I went to my rebbe. He knew of a better business deal in Moscow. So, of course, if my rebbe thinks I should go to Moscow, I'm on the first train. And, you know, had I invested in that deal in Warsaw I would be a very wealthy man today. And the money I invested in Moscow ... it's all gone."
The others looked shocked. "So nu, what's the miracle??"
"The miracle," he said, "is that I'm still a chasid."
See Vayikro 4 (22) “If a leader [of Israel] sins and unintentionally commits one of all the commandments of the Lord, which may not be committed,” to see that the Nosi (and by extension gedolei Yisroel) is/are indeed fallible.