Creating a single layer perceptron for the OR problem
The fact that you mention linear least squares error seems to hint that they want you to use a completely linear model $u_i=Wv_i$ for your perceptron. In this case you won't get exact answers like $0$ and $1$; you will only get approximations with some amount of error.

That said, I don't think a linear model makes sense for this problem, since it is a classification problem with two classes. Using a non-linear step-like function $f$ before the final output of a perceptron classifier is a pretty standard thing to do, so I see no problem with using $u_i=f(Wv_i)$. 

Assuming you can use $f$, using the weights $x_1 = x_2 = 1$ as you mentioned solve this problem exactly with zero error.