Humans do not have blood that is blue.
Despite the fact that some of us may have been told this in second grade and believe it because we can see our "blue" veins through our skin. Now, it didn't take me long to learn that blood was never really blue but this is a myth that is easily carried on and many still believe.
Of course, the argument is that we only ever see the blood as red because whenever it is leaving our bodies the air hits it and it immediately turns red then. It would be a huge breakthrough in science if the process were that simple. Some people so purely believe the blue and red blood myth that when there is a heart defect they then believe that the blue blood and red blood mixes making purple blood.
But... (and here's my post from that forum with one paragraph removed that apologized for length)
Deoxygenated blood is never blue. As a neonatal ICU nurse I’ve seen the ECMO pumps in action (a heart lung bypass machine that can allow for the heart and lungs to heal from injury) and air can not be allowed in the circuit that the blood runs through or it would cause major issues. I’ve seen both oxygenated and deoxygenated blood side by side this way and you have bright red and dark red.
Many times the belief that blood is blue comes from the fact that that veins are closer to the surface of the skin and the way light reflects off of them through the skin. Open the skin up but leave the vein intact and the vein does not appear blue at all.
As far as mixing blood in the heart, this happens when there is some type of defect in the walls separating the chambers in the heart or a valve does not work correctly allowing the blood to flow backwards through the valve. To be able to see this happening in real time in the actual heart, you would not see the difference in the reds because they would mix so well. If you have ever seen an ultrasound of the heart that has color on it (yes, the added colors are red and blue) that color is artificially added by the machine to help the technicians and doctors read the findings of it. The machine places the color by how the blood should ideally be flowing from the area it is detecting it.
Cyanosis, or the blue coloring around the mouth and beyond, when chocking or otherwise being oxygen deprived is once again just the way the vessels are then appearing through the skin and not to do with the color of blood.
I believe (this is truly my opinion) that some of the mistaken beliefs of colors of organs and such have come from anatomy texts that color coded everything to make the pieces easier to distinguish when studying, not because they looked that way in the body. For instance, most people have seen real skulls either through tv or museums and we all know that they do not have coloring such as this. It is just easier to see them in color than in black, white and shades of gray.
The wikipedia articles have blood explained pretty well with several links to legitimate medical papers and manuals that explain the reasoning behind it all if you really want to delve that far into papers and research.