Is it bad karma to disagree with an arhat? I just wondered, is it bad karma at all to disagree with an arhat? I'm not saying I would, I just wondered, because killing one is phenomenally bad!

What about disagreeing with a Buddha?
According to the Nibbedhika Sutta:


  "Intention, I tell you, is kamma. Intending, one does kamma by way of
  body, speech, &amp; intellect.


If you see this answer, bad karma or not, is related to the intentions of the individual. The story of the blind monk Ven. Chakkhupala in Dhammapada 1 and the story of the hunter's wife in Dhammapada 124 would serve as good examples from the scriptures.

If the individual has intentions that is insulting, disparaging or malicious towards the Buddha or arahant, then that would be generating bad karma.

However, if someone respectfully disagrees with the Buddha or arahant because he does not have the same view or understanding, then this should not be bad karma. If someone talks to a Buddha or Arahant, he should not incur bad karma, if he does so based on the principles of Right Speech (samma vaca), even if he disagrees with the opinion of the Buddha or the Arahant.

As said in the famous Kalama Sutta by the Buddha, just because a certain person is your teacher, it does not mean that you should simply accept what he or she says. Rather, it is preferable that you should accept the teachings only after you have known for yourself that it is good.


  "So, as I said, Kalamas: 'Don't go by reports, by legends, by
  traditions, by scripture, by logical conjecture, by inference, by
  analogies, by agreement through pondering views, by probability, or by
  the thought, "This contemplative is our teacher." When you know for
  yourselves that, "These qualities are unskillful; these qualities are
  blameworthy; these qualities are criticized by the wise; these
  qualities, when adopted &amp; carried out, lead to harm &amp; to suffering" —
  then you should abandon them.' Thus was it said. And in reference to
  this was it said.
  
  "Now, Kalamas, don't go by reports, by legends, by traditions, by
  scripture, by logical conjecture, by inference, by analogies, by
  agreement through pondering views, by probability, or by the thought,
  'This contemplative is our teacher.' When you know for yourselves
  that, 'These qualities are skillful; these qualities are blameless;
  these qualities are praised by the wise; these qualities, when adopted
  &amp; carried out, lead to welfare &amp; to happiness' — then you should enter
  &amp; remain in them.


Despite this, SN25 does have a provision for "faith followers" to meet a good end simply by having conviction and belief in the teachings of the Buddha, because it would lead them down the right track.


  "One who has conviction &amp; belief that these phenomena are this way is
  called a faith-follower: one who has entered the orderliness of
  rightness, entered the plane of people of integrity, transcended the
  plane of the run-of-the-mill. He is incapable of doing any deed by
  which he might be reborn in hell, in the animal womb, or in the realm
  of hungry shades. He is incapable of passing away until he has
  realized the fruit of stream-entry.


Nevertheless, the Buddha was a great teacher who managed to convince those who insulted and verbally abused him (see Akkosa Sutta), mocked him (see Kasi Bharadvaja Sutta) and intended to challenge or test him (see Dhananjaanii Sutta and Acela Sutta). Of course, there are also times when the Buddha knew when to give up trying to convince someone (see Kesi Sutta).

The Buddha also understood and empathized that the truth he discovered may not be easily understood by everyone (see Ariyapariyesana Sutta):


  "Then the thought occurred to me, 'This Dhamma that I have attained is
  deep, hard to see, hard to realize, peaceful, refined, beyond the
  scope of conjecture, subtle, to-be-experienced by the wise. But this
  generation delights in attachment, is excited by attachment, enjoys
  attachment. For a generation delighting in attachment, excited by
  attachment, enjoying attachment, this/that conditionality &amp; dependent
  co-arising are hard to see. This state, too, is hard to see: the
  resolution of all fabrications, the relinquishment of all
  acquisitions, the ending of craving; dispassion; cessation;
  Unbinding."


Also, don't forget that it may not be easy for unenlightened individuals to know who the Buddha really is, just like the case in the Dona Sutta and also the Ariyapariyesana Sutta:


  A second time... A third time, the group of five monks said to me, 'By
  that practice, that conduct, that performance of austerities you did
  not attain any superior human states, any distinction in knowledge &amp;
  vision worthy of a noble one. So how can you now — living luxuriously,
  straying from your exertion, backsliding into abundance — have
  attained any superior human states, any distinction in knowledge &amp;
  vision worthy of a noble one?'
  
  "When this was said, I replied to the group of five monks, 'Do you
  recall my ever having spoken in this way before?'


While the Buddha may be omniscient, the Arahants may not even recognize that the other is also an Arahant (see Bhaddiya Sutta). So, Arahants are not omniscient. They are only enlightened or freed from suffering.