1. Mayyim emtza’iyim – washing during the meal
Rav Naḥman explains that one is not obligated to wash between different dishes in the course of the meal, unless both a cooked (meat) dish and cheese are both being served, in which case washing would be necessary.
The Rashbam explains that Rav Naḥman is contrasting between a meal consisting of two dishes of meat or milk (where no washing is needed), and a meal where a milk dish is followed by a meat dish (where washing between them is essential). It is clear, however, that a milk dish could not possibly follow a meat dish, since that is forbidden. Rabbeinu Tam argues that Rav Naḥman is even talking about a meat dish that follows a milk dish. So long as there is no actual meat or milk products being consumed – all that is in the dish is a “taste” of meat or milk, there is no need to wash between them. Only when actual cheese is being eaten after meat would there be a requirement to separate them by washing.
The Rema accepts the Rashbam’s position, and it is common practice to wait a significant amount of time between meat dishes and milk dishes.
2. Mayyim aḥaronim – washing after the meal
Rav Yehuda the son of Rabbi Ḥiyya explains that it is essential to wash hands after the meal, as the salt – Melaḥ Sodomit – could blind you if there is any left on your fingers. Abaye adds that even if a small amount of this type of salt would become mixed with ordinary salt it would pose a serious danger.
It appears that the reference is to Magnesium Chloride (MgCl2), which can be found in large quantities in the Dead Sea. Both magnesium and chlorine can mix easily with the ordinary salt – Sodium Chloride (NaCl) – that is produced in Sodom near the Dead Sea. Since these are poisonous substances, someone who rubs his eyes with an unwashed finger could easily develop an infection.