May one polish his shoes?
Some Poskim rule it is permitted to polish shoes during Chol Hamoed. Other Poskim rule it is forbidden to polish shoes during Chol Hamoed. Some of these Poskim however permit doing so through a gentile. Practically, many are accustomed to avoid doing so. According to all, it is permitted to clean the shoes using a brush.
 See Chol Hamoed Kehilchasa 5/46; Piskeiy Teshuvos 541/4 footnote 16; Shemiras Hamoed Kehilchaso 14/24
 Milameid Lehoil 1/113-10; Yagel Yaakov 25; Chelek Halevi 181; Zeh Hashulchan 2/534; Pekudas Elazar 534; Shearim Hametzuyanim Behalacha 104/14; Shivilei David 534 permits only if another pair of shoes is not available; Rav Moshe Feinstein in Zichron Shlomo 4; Shevet Halevi 6/244 printed in Sefer Pnei Baruch Ohel Channah 3; Rav Elyashiv in Mivakshei Torah 106; Even Yisrael 5; Yabia Omer 1/32; SSH”K 66/48; Chol Hamoed Kehilchasa 5/46
 The reason: Polishing is not considered laundering and is a Maaseh Hedyot and is hence permitted to be done for the need of the Moed. [ibid]
 Kitzur Shlah Inyanei Asiyas Matzah; Shevilei David 534/1; Levushei Mordechai Telisai 10; Beis Shearim Hakdama; Yalkut Hagershoni 553; Chazon Ish, brought in Orchos Rabbeinu 2/122; See Piskeiy Teshuvos 541/4 footnote 16; Poskim in Shemiras Hamoed Kehilchaso ibid footnote 85
 The reason: As it is included in the laundering prohibition. [Shevilei David ibid]
 Yalkut Hagershoni 553; Yagel Yaakov ibid rules that although it is permitted to be done it is best to do so through a gentile.
 Chelek Halevi ibid; Yagel Yaakov ibid; Betzel Hachochmah 5/95; Beir Moshe 7/63; Tzitz Eliezer 8/15-14
 Shevet Halevi 6/244 printed in Sefer Pnei Baruch Ohel Channah 3; Chol Hamoed Kehilchasa 5/45