Using the same Knife sharpener for meat and dairy knifes:[1]

It is permitted to use the same knife sharpener for sharpening both dairy, meat and Pareve knives.[2] This applies whether the sharpener is made of metal, stone, and applies to both a hand and electric sharpener. Prior to sharpening the knife, one is to clean the blade well and wash down the sharpener.[3] Some write that the knife and sharpener should be dried prior to the sharpening, if the sharpener gets very hot as a result [i.e. Yad Soledes].[4] Despite the above letter of the law allowance, some conclude that it is proper not to use the same knife sharpener for meat and dairy knives.[5]

Knife sharpening stores: When bringing a Kosher knife to a knife sharpening store, one is to make sure that the knife is not immersed into a hot water bucket, as is done in some facilities. Likewise, one is to make a sign on the knife to make sure upon pickup that it is indeed the same knife that he gave in.  

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[1] See Michaber Y.D. 121:7; Beis Yosef 122:9-10; Beis Yosef 122:9-10; Shevet hakehasi 4:162 [permits only without much liquid]; Sefer Hagalas Keilim 13 footnote 260; Hakashrus 2:44

[2] Pashut, as there is no reason to prohibit the use of a sharpener for both meat and dairy knives. Taste cannot transfer from one vessel to another without heat and liquid, and the act of sharpening does not create Halachic heat, and even if it did, two dry vessels do not transfer taste even when hot. Furthermore, the Michaber in Y.D. 121:7 rules that sharpening a Treif knife is a form of Koshering, and thus if it can Kosher a Treif knife, certainly it can be used for sharpening a meat/dairy knife. No mention is ever made in the Poskim that the sharpener must only be used for one form of Kosher knives! Furthermore, the Beis Yosef 122:9-10 brings in the name of the Mordechai Avoda Zara 832 that people would bring their knives to a gentile sharpener, and if the knife was returned within the hour, the knife is Kosher, and no worry is mentioned regarding the sharpener itself having been used for Treif knives.

[3] As if the blade contains Charif residue, it could cause the meat/dairy taste to get absorbed into the vessel, and then back into the knife. See Chapter 5 Halacha 3 in Q&A regarding a cutting board.

[4] See Shevet Hakehasi ibid

[5] Sefer Hagalas Keilim 13 footnote 260; Hakashrus 2:44; See Piskeiy Rabbeinu Yechiel Miparitch 47 and Shevet Hakehasi ibid that sharpening creates Yad Soledes heat. Vetzaruch Iyun!