Berachot 52: The Implications of Beit Shammai or Beit Hillel's Opinions

We continue to discuss yesterday's new Mishna.  The rabbis question whether we should side with Beit Hillel's opinion or Beit Shammai's arguments in yesterday's daf.  We know that unattributed Mishnayot are attributed to Rabbi Meir.  We also know that Beit Hillel tends to be more lenient while in this yesterday's debates, Beit Shammai was more lenient.  

The rabbis discuss whether or not the cup of wine is valid after wine has been removed.  What if the cup contained less than the minimum amount of wine required?  This conversation leads them into a debate about vessels and ritual impurity.  What if one touched a creeping animal with one's hands and then touched the cup to say the Grace after Meals?  Will one transfer that ritual impurity to the cup?  One's hands would take on the status of second degree ritual impurity.  If the outside, rim and handles are ritually impure, the inside and liquid can continue to be ritually pure.  The rabbis consider a drop of liquid that might fall from the inside of a ritually impure vessel, too.

After washing one's hands, one dries them on a towel.  The rabbi wonder whether the towel is placed on the table or on a seat cushion.  As it is wet, the towel could become ritually impure from the cushion and then transfer ritual impurity to anyone else who touches it.  What about placing the towel on the table?  If the table has second degree ritual impurity, anything that touches the table will become ritually impure.  

Crumbs that are smaller than an olive bulk are not considered to be actual food, and so we do not waste them if we sweep them away.  In their further discussions, the rabbis agree that the meaning of bara and boreh, are both created.  Perhaps the argument between Beit Hillel is between whether there are lights of the fire (Hillel) or light of the fire (Shammai).  

Could spices of Gentiles be restricted because those spices might have been intended for use with idolatry?