When kashering (through hagoloh iruy keli rishon) a surface such as table, kitchen counter, etc., does one need to ensure it is totally dry after every sheficho (see Mishnah Berurah siman 451 seif katan 50)? Many thanks!
The surface does not have to be totally dry – it can remain damp – but it should not be actually wet with water that has cooled (as you rightly note from the Mishnah Berurah). The reason for this is that the hot water falling on the surface will be cooled by the cold water on the counter, and with therefore not be effective for kashering.
If a significant amount of water is poured, it won’t be necessary to dry the surface, because the water will heat up with the initial pouring, and the water that comes after will not be cooled.