Can I sue a landlord with a sub-par home?

Yes, provided that you can prove that he knew or should have known about the defect that caused the injury and had an opportunity to fix it before your injury, but failed to do so. Also, depending on exactly what happened, a portion of the responsiblity may be assessed against you. In other words, it could be found that you were 20% or 40% or "X"% responsible for your own injuries.