A relatively small hole on a washing cup will render it invalid. The minimum size is large enough to allow water to enter the cup from outside, which is slightly bigger than the size of a hole that would cause water to drip out from inside the cup.
The minimum size for a washing cup to be acceptable is one revi'is, which is equivalent to 86cc or 3 oz. Larger than this is certainly preferable.
Nat all cups are valid, there are many details in these halachos which are outside the scope of this forum.