Good question.

Let’s start by talking about how oxygen travels in our blood. Each mature red blood cell is basically a bag of hemoglobin. Hemoglobin contains protein and iron and each molecule has places for 4 oxygen molecules. The hemoglobin drops off oxygen where it’s needed--at the cells. It then travels back to the heart, then the lungs, and loads up with oxygen. It goes back to the heart to be sent out to the cells again.

Sometimes it’s easier to think about questions using an analogy about something we’re familiar with. Think about the red blood cells like delivery trucks. They load up in one place, like a warehouse. That’s like our lungs. Then they deliver the goods to where they’re needed, like a home or store. That’s like our cells. Here’s where the analogy doesn’t quite fit; smart people make sure the trucks get completely loaded and unloaded. Oxygen just enters and leaves the red blood cells due to diffusion, which is a random process. If the red blood cells are near a place with low oxygen, a bunch of the oxygen tends to leave, but not all of it. When the red blood cells are in a place with high oxygen, they tend to fill up with oxygen, but are never 100% full, or saturated. About 96-99% is usual for a healthy person at sea level. Even deoxygenated blood has oxygen in it, but the hemoglobin spaces are just a lot less than 99% full. How full they are depends on how low the oxygen levels were in the cells. A working muscle cell or a brain cell needs a lot of oxygen. A fat cell usually doesn’t.

Medical professionals can measure the percent oxygen saturation of your blood using a device that clips painlessly on your finger.

Back to your question, what do you think would happen if some of the trucks went back to the warehouse half full? What would happen if you sent some half-empty trucks to the homes and businesses waiting for products? A lot less stuff would get delivered. When oxygenated and deoxygenated blood mix, less oxygen gets delivered to the tissues. This can happen when there’s a hole in the wall that separates the right side of the heart (deoxygenated blood) from the left side (oxygenated blood).

Before we were born, our lungs didn’t really do anything. We got our oxygen from our mothers. Our mothers breathed in oxygen, their blood took it to the placenta (and all over their bodies), and oxygen left our mothers’ blood and went into our blood. The placenta is attached to the umbilical cord, so our belly buttons used to be our supply line for oxygen. Because our lungs were deflated, there was a hole in the wall between the sides of the heart so that blood could skip the lungs. When we took our first breaths, a flap closed over the hole and “patched” it. Some babies still have a full or partial hole in that wall. Sometimes people call this a “hole in the heart.” It causes the blood to mix. Depending on how open the hole is, the baby could be fine, or they could have trouble getting enough oxygen. This heart problem can be fixed.

Can you think of anything doctors could measure that would help them figure out if a baby had a heart defect like that?

Mixing of oxygenated and deoxygenated blood in and of itself does not do much. In oxygenated blood, oxygen is bound to hemoglobin inside of the red blood cells, and in deoxygenated blood those hemoglobin sites are empty. [As far as I can find] The two quantities would simply mix. The more important considerations are what this mixing means for the organism. Mixing of oxygenated and deoxygenated blood would lead to a reduction in the oxygen per volume of blood, potentially leading to hypoxemia (below-normal oxygen in the blood, or low oxygen saturation).

If blood is less saturated with oxygen, then less oxygen is transported to the rest of the body. Since sufficient oxygenation of an organism's cells is essential to survival, the body tries to correct for this by pumping more blood (to prevent the very similarly named hypoxia, which is too little oxygen in the body tissues). Thus, some of the symptoms of mild hypoxemia is elevated heart rate and blood pressure. In more severe cases, heart rate and blood pressure can fall (seems to be implied that this is because insufficient oxygen is reaching the muscle cells to pump blood), brain function is impaired, and cyanosis (bluish discoloration due to deoxygenated blood being less red (but still red) than oxygenated.

In cases of prolonged hypoxemia, this extra work by the heart often results in thickening of the pulmonary arteries (thereby restricting blood flow and thus increasing blood pressure), higher blood pressure in the lungs, and failure of the right side of the heart.

Blood distribution becomes less efficient, since the body tissues are only getting half the oxygen they would if you kept the two separate. Notably, apart from archosaurs (birds, other dinosaurs, crocodiles, pterosaurs) and mammals, mixing of blood happens in vertebrates. However, apart from archosaurs and mammals, vertebrates are cold-blooded, so they don't need as much oxygen.