Why am I getting a wrong output when implementing Feige-Fiat-Shamir ID protocol?
The first problem is, that you calculated $v_i$ wrong right at the start.
$$v_i = s_i^2 \mod n$$
This means:
$$v_1 = 5^2 = 25 \mod 77$$
$$v_2 = 12^2 = 67 \mod 77$$
$$v_3 = 37^2 = 60 \mod 77$$

Then at the end you have: 
$$(x \cdot \prod_i v_i^{a_i})  = 67 \cdot 25 \cdot 1 \cdot 1 = 58 \mod 77$$