My dad gave me his old recurve yesterday. This is the first bow I shot, or tried to shoot, when I was young. Could finally pull it back when I got a bit older and shot it quiet a bit at home and took it hunting a few times. As you see in the pictures there is some cracking of the finish on the limbs. I think this bow belonged to my uncle way back in the day. My dad said this is the second bow because my uncle sent the first one back when it was new due to the cracking. I believe the cracks have been there since the 70's. Is this something to worry about if I wanted to shoot it or should I get this repaired?

I wouldn't worry about it....its made it this long, it's probably fine... you could lightly  sand it with 220 sand paper and refinish it easily though...

It's only in the old finish. JF