If you hit an artery there is the possibility of heart attack or stroke. But hitting an artery is very unlikely, and if you aspirate you will know that you have before you actually push in the plunger. Bruising is common. Abscesses are fairly rare, but not unheard of. Infections and blood poisoning are possible, but again, there are precautions to take against that. Some people have allergic reactions to the oil used to carry the hormones. Hmmm. Am I missing anything?
The difference is, if you follow the correct procedure, the likelihood of having problems with injections is pretty low. Whereas, oral hormones, for instance, have a very high likelihood of liver damage, over time.
And to answer the OP's question, I chose to do mine weekly in order to lessen the hormonal roller coaster effect. YMMV.