Scrubbing, Shining and Polishing dishes and silverware:
One may scrub down, shine and polish all dishes and cutlery needed to be used on Shabbos, even if they are made of silver, so long as the shining agent does not remove any layer of the vessel. Thus it is forbidden to clean or shine silver using a material which will inevitably remove a layer of the silver from it. [See Q&A regarding removing tarnish from silver!]
One may polish all vessels on Shabbos if the following two conditions are fulfilled:
- He is doing so in order to use the vessel that Shabbos
- The polishing will not inevitably remove any of the material of the vessel.
Q&A on Polishing
May one polish glass dishes?
May one polish silverware, copperware and other silver vessels?
It is forbidden to remove tarnish from silverware or copperware on Shabbos. If there is no tarnish and one simply desires to shine the vessel it is permitted to do so even if it is made of silver or copper. However some Poskim rule it is forbidden to polish metal vessels in all cases, even with a dry cloth, and even if there is no tarnish.
Using a silver polish cloth: It requires further research to verify whether silver polishing cloths accomplish the shine through removing the silver material or not. If the former is the case then according to Admur it may be used. If the latter is the case it may not be used being it removes material from the silver.
Using silver polish cream: It is forbidden to use any polishing cream to polish vessels due to the smearing prohibition.
Using a wet sponge: When using a sponge with water to polish a vessel one must be careful to only use a permitted type of sponge, as explained in the previous Halacha.
May one remove rust from metal, such as from the blade of a knife?
 Silver is soft and can have layers of it rubbed off during polish. Doing so is forbidden due to the Memacheik/Smoothening prohibition. Now although one has no intention to remove a layer of the silver and smoothen it, but rather simply to shine it, nevertheless this is an inevitable occurrence and is hence forbidden. It is however permitted to polish the silver using soap and the like which do not inevitably remove the silver, as even if it happens to do so, since this is not inevitable and one did not intend to do so, it is therefore permitted. [ibid]
 Admur 323/11; SSH”K 12/24
Other Opinions: The Mahril rules it is forbidden to polish glass dishes using oats. The M”A 323/15 questions as to why this should be forbidden and suggests that perhaps only washing dishes from dirt did the Sages allow, however to polish is forbidden. He concludes with a Tzaruch Iyun. Admur completely omitted this ruling of the Mahril hence implying it is allowed. SSH”K 12/24 in name of Rav SZ”A rules it is allowed, as even according to Mahril it was only prohibited to polish using oats. Tehila Ledavid 323/17 however explains it is forbidden to polish all vessels due to Tikkun Keli.
 Mahril brought in MA 323/15; Tehila Ledavid 323/17 brought in previous footnote; Toras Shabbos 323/9
 As tarnish is an actual layer of the metal which has corroded, and its only form of cleansing is removal.
 Admur rules [323/11] that it is permitted to be done so long as one is not using an item which will inevitably remove a layer of silver or copper from the vessel, and is doing so simply to shine the vessel and not remove tarnish, as stated above.
 SSH”K 12/24 based on Tehila Ledavid 323/17.
The SSH”K learns as does the Tehila Ledavid in the Mahril brought in M”A that the action of polishing metal vessels is forbidden on Shabbos due to Tikkun Keli. Admur clearly however does not learn this way, and likewise omitted the entire ruling of the Mahril as stated above.
 Tehila Ledavid 323/17
 This is forbidden possibly due to the Mimacheik and Tochein prohibition. [ibid]