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The extra red blood cells make your blood thicker than normal. As a result, blood clots can form more easily. These clots can block blood flow through your arteries and veins, which can cause a heart attack or stroke. Thicker blood also doesn't flow as quickly to your body as normal blood.
People taking blood thinners are more at risk from this type of damage since their blood clotting is already restricted. Injections can also be the cause of subcutaneous hematoma (which I get on a regular basis from my medication, Clexane). When an injection punctures the skin on the tummy or thigh it can graze, or pierce straight through, a blood vessel causing blood to seep out into the fatty tissue. If you're injecting Heparin or blood thinners, this can make hematoma worse because your clotting is restricted. Source.