El error está en la línea 3. Debería ser así:
$$ \ overline {(x_3 + x_2) x_2} = \ overline {(x_3 + x_2)} + \ overline {x_2} = \ overline {x_3} \ cdot \ overline {x_2} + \ overline {x_2} = \ overline {x_2} (\ overline {x_3} + 1) = \ overline {x_2} $$
Esto te da:
$$ x_4x_2 + \ overline {x_2} + x_2x_0 = x_2 (x_4 + x_0) + \ overline {x_2} $$
Para simplificar esto, podemos escribir:
$$ \ overline {\ overline {x_2 (x_4 + x_0) + \ overline {x_2}}} = \ overline {(\ overline {x_2} + \ overline {(x_4 + x_0)}) \ cdot x_2} = \ overline {\ overline {x_2} \ cdot x_2 + \ overline {(x_4 + x_0)} \ cdot x_2} = $$
$$ = \ overline {0+ \ overline {(x_4 + x_0)} \ cdot x_2} = (x_4 + x_0) + \ overline {x_2} $$
que es igual a \ $ x_4 + x_0 + \ overline {x_2} \ $.
Siempre puedes escribir un programa en C simple para ver dónde te equivocaste.
Aquí tienes:
#include <stdio.h>
#include <stdint.h>
int main(void) {
uint8_t byte;
/* A number of all possible combinations.
For 5 variables it would be 0b11111 etc. */
uint8_t MAX = 0b1111;
/* Print header */
printf("x4 x3 x2 x0 | f1 f2 f3 f\n");
for (byte=0; byte<=MAX; byte++)
{
/* Get individual bits (combinations) */
uint8_t x0 = (byte & (1<<0)) >> 0; /* my x0 is your x0 */
uint8_t x1 = (byte & (1<<1)) >> 1; /* my x1 is your x2 */
uint8_t x2 = (byte & (1<<2)) >> 2; /* my x2 is your x3 */
uint8_t x3 = (byte & (1<<3)) >> 3; /* my x3 is your x4 */
/* Logic functions */
uint8_t f1 = (x3 && x1) || !((x2 || x1) && x1 && 0b1) || (x1 && x0);
uint8_t f2 = (x3 && x1) || !((x2 || x1) && x1) || (x1 && x0);
uint8_t f3 = (x3 && x1) || !(x2 && x1) || (!x1) || (x1 && x0);
/* Final solution */
uint8_t f = (!x1) || x0 || x3;
/* Print truth table */
printf(" %d %d %d %d | %d %d %d %d", x3, x2, x1, x0, f1, f2, f3, f);
/* Print wrong line indicator */
if ((f2!=f1) || (f3!=f1) || (f!=f1))
printf(" <");
printf("\n");
}
return 0;
}