PS 3 #2c) Many people said that since T is 1 to 1,  L(T(v1)) = L(T(v2)) 
implies that T(v1) = T(v2), which is not always the case.

PS#3, 5: lots of them only prove one direction i.e. one set
is a subset of the other, but neglect the other direction. make sure to prove
both directions when proving two sets are equal.
 

PS 4 #1b) A lot of people showed that L(0v) in  V when they needed to show 
L(0v) is in   {0v}

PS 4 #3b) A common problem was only taking T(u), not T(T(u)), 
Also, people often used the "is an element of" symbol  in place of "is 
a subset of" symbol and vice-versa. You may want to go over the 
difference quickly in class. (this was a problem on the midterm as well)