Top pic just looks like some weather checking (also called "rain checking" or "fruit russeting"). It's just superficial damage to the tomato's epidermis. Second picture looks like rot is starting where insect pests have done some damage, or it might be something like anthracnose setting in.

There isn't much that can happen to a tomato that will be any danger to humans unless there is mold growing in it. It's really more a question of whether taste is negatively affected so that the fruit isn't worth eating anymore. I would eat the fruit in the first pic normally. The fruit in the second pic looks like it's probably verging on overripe in addition to having those soft spots. If I were making a dish with cooked tomatoes, I'd cut off the affected parts and cook the remainder. Otherwise, I'd probably chuck it in my worm bin just because I suspect the taste would be inferior.

One real danger is canning fruit that has certain kinds of damage, as some kinds of damage can lead to fruit that is less acidic, and the higher pH can affect the safety of canned food by allowing dangerous bacteria to grow that are normally kept in check by acidity. There is plenty of information available on the web about that if you're interested in canning.