user609: I've heard it said that Popes are infallible,(whether one believes this or not). 
Although the arahant has removed all the defilements, can they still be wrong, make mistakes, or are they all-knowing? I vaguely remember a story of an arahant playing a dirty trick on his less than wise brother? 

user295: Yes and no in the case of infallibility.
Infallible - what ever they do their actions do not created new conditioning. The actions are not based on the 3 unwholesome roots.
Fallible - though the actions are not based on unwholesome volition, they may not always be the optimal or best cause of action. Their infallibility is based on the fact they are never wrongly motivated, though the outcome of any action may not always have the desired or optimal results and also some action can be done differently to make a bigger impact.
They know the cause and effect regarding the mind and matter process hence understanding enough about the cause of misery and the elimination of misery.

user-1: It depends on what you refer to as "mistake", "wrong" and "all knowing".
For example, the first known schism [1] brought 5 points to discussion, 4 pertaining to arahants:

1: that an arahant can be seduced by another person
2: that an arahant may be ignorant of some matters
3: that an arahant may be in doubt
4: that an arahant may receive (be instructed by) another person

A case can be made against (2) and (3) from the suttas if the matters in question are limited to nirvana and the doctrine -- which is more than reasonable. Omniscience as "knowing everything continuously" can be refuted by the suttas as well -- the Buddha not only said he did not have that power, but he declared it was impossible for a person to have it. From that standpoint, I guess (4) would make little sense to discuss further. But (1) did not reach consensus.
EDIT: For an examination of Buddha's omniscience from the suttas, see analayo's paper on the subject.
[1] A.K. Warder, Indian Buddhism.

609: <p>I've heard it said that Popes are infallible,(whether one believes this or not). </p>

<p>Although the arahant has removed all the defilements, can they still be wrong, make mistakes, or are they all-knowing? I vaguely remember a story of an arahant playing a dirty trick on his less than wise brother? </p>
 295: <p>Yes and no in the case of infallibility.</p>

<p>Infallible - what ever they do their actions do not created new <a href="https://en.wikipedia.org/wiki/Sa%E1%B9%85kh%C4%81ra" rel="nofollow">conditioning</a>. The actions are not based on the <a href="https://en.wikipedia.org/wiki/Three_poisons_(Buddhism)" rel="nofollow">3 unwholesome roots</a>.</p>

<p>Fallible - though the actions are not based on unwholesome volition, they may not always be the optimal or best cause of action. Their infallibility is based on the fact they are never wrongly motivated, though the outcome of any action may not always have the desired or optimal results and also some action can be done differently to make a bigger impact.</p>

<p>They know the <a href="http://en.wikipedia.org/wiki/Prat%C4%ABtyasamutp%C4%81da" rel="nofollow">cause and effect</a> regarding the <a href="http://en.wikipedia.org/wiki/Namarupa" rel="nofollow">mind and matter process</a> hence understanding enough about the cause of misery and the elimination of misery.</p>
 -1: <p>It depends on what you refer to as "mistake", "wrong" and "all knowing".</p>

<p>For example, the first known schism [1] brought 5 points to discussion, 4 pertaining to arahants:</p>

<ul>
<li>1: that an arahant can be seduced by another person</li>
<li>2: that an arahant may be ignorant of some matters</li>
<li>3: that an arahant may be in doubt</li>
<li>4: that an arahant may receive (be instructed by) another person</li>
</ul>

<p>A case can be made against (2) and (3) from the suttas if the matters in question are limited to nirvana and the doctrine -- which is more than reasonable. Omniscience as "knowing everything continuously" can be refuted by the suttas as well -- the Buddha not only said he did not have that power, but he declared it was impossible for a person to have it. From that standpoint, I guess (4) would make little sense to discuss further. But (1) did not reach consensus.</p>

<p><strong>EDIT</strong>: For an examination of Buddha's omniscience from the suttas, see <a href="http://www.buddhismuskunde.uni-hamburg.de/fileadmin/pdf/analayo/BuddhaOmniscience.pdf" rel="nofollow">analayo's paper on the subject</a>.</p>

<p>[1] A.K. Warder, <em>Indian Buddhism</em>.</p>
