Pesachim 59 a, b

The rabbis are in deep discussion regarding sacrifice of the Paschal lamb, general halachot regarding sacrifice, and the importance of intention with regard to this rite. 

• the sacrifice of the Paschal lamb
• when the sacrifice should occur: meanings of "in the evening" and "in the afternoon"
• rites that are valid "from evening to morning"
• the order of occurrence: lighting lamps, burning incense, sacrificing the Paschal lamb
• how one word might determine our rites, for example, the word "it" in  Exodus 30:8: "And when Aaron lights the lamps in the afternoon he shall burn it" might suggest that the incense is already burning when one lights the lamps.
• what delays these rituals (the  immersions of a zav, one who lacks atonement on other days, the strength of the positive mitzvah to eat sacrificial meat, etc.)
• when birds alone are used as sacrifices
• when animal sin-offerings are left atop the altar to be sacrificed in the morning (and thus observing the positive mitzvah of completion)
• the sacrifices brought by a zav
• the sacrifices brought by a woman following childbirth
• what priests may eat after the sacrificial parts are offered (breasts and thighs)
• requirements of full atonement
• different requirements for ritually impure offerings and for fat
• different requirements for Pesach offerings
• the requirement that Shabbat and Festival burnt-offerings are not shared

In a new Mishna, we are taught that a priest must intend to sacrifice  either a peace-offering or a burnt-offering or a Paschal lamb at all stages of the offering for it to be valid.  Rav Pappa raises a question in the Gemara: did the priest in question have two different intentions during one of the four rites of one offering?  Or, perhaps, did he have two different intentions during the first and third parts of the offering?

• Steinsaltz tells us of three types of disqualifications:  
• when blood is sprinkled/limbs are burned at the wrong time (thus the sacrifice will be rendered piggul).  
• when the place of sacrificing is incorrect.  
• only applies to sin-offerings and the Paschal lamb: when the sacrifice is offered with an incorrect intention. 

• The four rites that can disqualify an offering regarding intent are:
• slaughtering the offering
• receiving its blood in a consecrated vessel (collected in a vessel from the neck)
• carrying the blood to the altar 
• sprinkling the blood on the altar (of great consequence regarding atonement)

• Steinsaltz shares a fascinating note regarding Rabbi Yosei's idea regarding sacrificial animals:
• a person is accountable the conclusion of his statement
• if one intended to make both statements but must say one first, then the second is valid
• if he changed his mind after the start of his first statement, the conclusion is irrelevant
• simply making the first statement changes the status of the animal in question
• one may retract one's statement in other halachot for changing his mind

• Rabbi Shimon ben Nannas believes that only the conclusion of one's statement is the most important part of the statement as it holds the person's intention

It is wonderful to note the rabbis' concerns regarding intention. No one can measure another's intention.  This is an internal process.  Thus priests could lie about their thoughts and feelings at the time of sacrifice and no one would know the difference.  Often we are told that rabbis and priests are vigilant - in today's daf,  kohanim zrivin hen.  They are understood to hold themselves to a higher standard that the rest of us.  But who knows whether or not another person, even a priest, is vigilant in his heart?