We may earn money or products from the companies mentioned in this post.
I have been fortunate that my family has kept several boxes full of old photographs. Most are in good condition, but some are falling apart. 
This old photograph of my Grandma Ola as a young women is crumbling apart. You can see where pieces of the photo have been taken out completely. I have several different photo software programs that can help repair, my favorite is a free program that I find the easiest is to learn with Photoscape.
Here is a screenshot of Photoscape and where to find Clonestamp to correct these flaws.
I have added arrows to the sections you will want to click on to fix. Once you have selected the clone stamp in tools, you will want to click first on an area that is not damaged that matches the area that is damaged. A circle will appear, locking in the undamaged area. Then using your mouse click over the damaged area. This will clone the undamaged area to the area needing to be fixed. Giving your this result.
The amount of cracks and damage on this intense and I am still working on it. However you can notice the wholes are no longer visible and most of her cheeks are repaired. Here is another one I have fixed of my Great Aunt Lovella and Uncle Earl
Before
After
The program is simple and free to use. No real complex techniques to learn with Photoscape.
Follow me on the web!