When one is visiting the western wall, what are some specific halachos that he/she should be cognizant of?
By "specific halachos" I mean halachos that only apply to the Kosel -- and not anywhere else.
The first question in Halacha at the Kosel is whether, how, and when you have to do Kriyah at the Kosel.
This link http://www.thekotel.org/content.asp?Id=138 discusses the following 4 topics in Halacha at the Kosel.
Leaving the KotelCam open on Shabbos.
Is there a problem with saying Nishmas on a daily basis - which is what is done at the Kosel every midnight.
Going through the metal detectors at the Kosel on Shabbos.
Whether you may carry at the Kosel on Shabbos.
This link http://www.din.org.il/2011/02/01/%D7%A4%D7%A8%D7%A9%D7%AA-%D7%AA%D7%A8%D7%95%D7%9E%D7%94-%D7%94%D7%9C%D7%9B%D7%95%D7%AA-%D7%94%D7%9B%D7%95%D7%AA%D7%9C-%D7%94%D7%9E%D7%A2%D7%A8%D7%91%D7%99/ discusses
whether an unpure person (Adam Tamei) may go to the Kosel
whether you may put your fingers or papers between the stones
whether you may have benefit from the stones.
See this link http://www.din.org.il/files/newsletter/he_45.pdf for some more Kosel Halachos.