Shortest Unique Substrings
Python 3, 124 123 111 96 bytes
f=lambda s,n=1:[x for x in[s[i:i+n]for i in range(len(s)+1)]if s.find(x)==s.rfind(x)]or f(s,n+1)

Looks for strings such that the first occurrence from the left is the same as the first occurrence from the right. The +1 in the range is to accommodate for the empty string case.
Now if only Python had a .count() which counted overlapping matches, then this would have been a fair bit shorter.