1) COUNTING JEWS
QUESTION: The Gemara relates that a system of lots was used to select which Kohanim would perform which Avodos in the Beis ha'Mikdash each day. The Gemara quotes the Mishnah in Yoma (22a) which describes the system of lots. As the Gemara there explains in more detail, one appointed Kohen would choose and say aloud a random number, and then he would count the Kohanim up to that number. The Kohen with whom the count ended was awarded that job. The Gemara teaches that the appointee would not point to and count the Kohanim themselves. Rather, each Kohen would extend one or two fingers, and the appointee would count their fingers. The Gemara in Yoma (22b) explains that the count was performed in this manner because it is forbidden to count the Jewish people (as derived from the census of the people taken in the Midbar, where the count was made by collecting a half-Shekel from each person and then counting the coins).
The commentators address the question of why David ha'Melech counted the people directly (as related in Shmuel II, ch. 24). Indeed, David ha'Melech was punished for attempting to count the Jewish people. How, though, did David ha'Melech make such a mistake, violating an explicit prohibition in the Torah (Shemos 30:12)?
ANSWERS:
(a) The RAMBAN (Shemos 30:12) explains that David ha'Melech thought that the prohibition against counting Jews directly applied only in the Midbar, when there was an additional need for the coins given for the census (in order to fashion the Adanim for the Mishkan from the coins). He mistakenly understood that it was not a commandment binding for all generations.
(b) The MIZRACHI (ibid.) explains that David ha'Melech understood that the coins in the Midbar were not given as a means by which to count the Jewish people. Rather, he thought that a regular census indeed could have been conducted, after which a half-Shekel had to be given as a Kofer Nefesh in order to avoid the plague that would otherwise follow due to the Ayin ha'Ra of the count.
(c) The BE'ER SHEVA explains that Hash-m caused David ha'Melech to make this mistake as a punishment for something else that he had done. The Gemara in Berachos (62b) relates that Hash-m told David, "You said that I 'persuade' people to sin? I will punish you by having you forget something that even children know...." There was a Divine decree for David to forget the verse on this single occasion.
2) WASHING THE HANDS AND FEET BEFORE TOUCHING A VESSEL OF THE BEIS HA'MIKDASH
OPINIONS: The Mishnah discusses the procedure performed by the Kohen who won the right to remove the coals from the Mizbe'ach (Terumas ha'Deshen). The Mishnah relates, "They say to him: Be careful not to touch the Kli until you have sanctified your hands and feet from the [water of the] Kiyor." (See TIFERES YISRAEL #48, who explains that the heads of the Beis Av said this warning to him. See BARTENURA, who explains that the "Kli" was the Machtah (coal-pan) with which the coals and ashes were removed from the Mizbe'ach.)
Why was it necessary to warn the Kohen specifically about this law?
(a) The MEFARESH (DH Mi she'Zachah) writes that the Kohen certainly knows that he may not touch the Kli before washing his hands and feet in the Kiyor. Nevertheless, the Mishnah requires that he be warned not to touch the Kli, because the Terumas ha'Deshen is performed by a single Kohen who goes to do it alone, with no one to remind him, and he might forget and touch the Kli before washing his hands and feet.
(b) The MAHARI KURKUS (Hilchos Temidin u'Musafin 2:12) explains that it is necessary to warn the Kohen specifically not to touch the Kli before washing his hands and feet in the Kiyor, because the Kohen might think that removing the ashes from the Mizbe'ach is not an important Avodah and does not necessitate the washing of the hands and feet.
(c) The TOSFOS CHADASHIM (on the Mishnah) writes that Kohanim who have never before performed the Avodah might not know the Halachah that one must not touch the Kli before washing. Since the novice Kohanim must be warned, the practice is to warn all of the Kohanim about it. The Tosfos Chadashim proves this from the fact that the Mishnah also says that they tell the Kohen that the Machtah is to be placed in the corner, between the ramp and the Mizbe'ach, on the western side of the ramp. Clearly, this instruction was given for the sake of the Kohanim who have never before performed the Avodah of Terumas ha'Deshen.
(d) The RA'AVAD writes that the reason they tell him not to touch the Kli is not that the Kli will become Pasul if he touches it. The Kohen is completely Tahor (especially since he immersed in the Mikvah before performing the Avodah, as the Mishnah (26a) says) and he cannot make a Kli Shares become Tamei by touching it. Rather, the reason why he is not permitted to touch the Kli is that he might forget and perform the Avodah itself before he washes his hands and feet. There is no prohibition against touching a Kli before washing, but there is a prohibition against performing an Avodah before washing. It is because of this prohibition that the Kohen is warned not to even touch the Kli. (See also BARTENURA.)
(e) The TIFERES YISRAEL (Boaz #3) also explains that there is no intrinsic prohibition against touching the Kli before washing. Rather, this measure was enacted to prevent a different prohibition from occurring. Since the Kohen has so much zeal and love for the Avodah, there is a concern that he might forget to wash first before he performs the Avodah. The Tiferes Yisrael writes that for this reason the Gemara in Yoma (end of 24b) says that the Kohanim perform the Payis (lottery) while wearing Bigdei Kehunah; if they would perform the Payis while wearing ordinary clothes of Chulin, there would be a fear that the Kohen who wins the lottery might run to do the Avodah out of his ardent enthusiasm and forget to change into Bigdei Kehunah.
(f) Perhaps we may suggest another answer, according to the words of the Mefaresh (DH Ad she'Yekadesh). The Mefaresh explains that the reason why the Kohen must wash his hands and feet in the Kiyor before he does the Terumas ha'Deshen is that the passing of the night ("Linah") causes the previous day's washing to become null, and therefore he must wash again in the morning. The Mahari Kurkus (loc. cit.) quotes the RAMBAM (Hilchos Bi'as ha'Mikdash 5:6) who says that even if the Kohen was awake all night, and even if he had washed during the night in order to burn the Chalavim on the Mizbe'ach, he still must wash again in the morning.
Perhaps the Kohen must be warned to wash his hands and feet before touching the Kli because he might mistakenly think that his washing of the previous day, or his washing during the night, is still valid. (D. BLOOM)

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