What kind of complications might happen from an upper extremity joint mri with dye?

Very rare: Complications from arthrogram for MRI is rare. I do many of these and the most common side effect is simply soreness from the injection. There is a theoretical risk of kidney damage, but the amount of contrast used is so small, this is very unlikely. If the dye is given intravenously, it might slightly raise this risk. Other rare complications include bleeding and infection.

Many: There are many complications for this, mostly related to the injection of contrast. Fortunately, the number of complications is small, and pre-screening for risk factors is helpful. You can get infection at the injection site, deep vein thrombosis, embolism, septicemia and more. You can have an allergic reaction to the contrast, from mild to very severe and death, or have kidney damage.