Alot depends on the severity of the damage. A small stain on a ceiling for instance, versus an area where the ceiling is now lying on the floor. Appraisers are required to note any "deficiencies" in a property, and depending on the loan program, this could be a cause for a rejection. Do you have verification that the leak has been repaired? Do you like the home well enough that if there was an appraisal issue, and the current owner would allow you entry into the property (after executing a "hold harmless agreement) to repair the damage-some asset managers will allow this, you could proceed with the purchase after the repair was completed & reinspected by the appraiser. Sometimes this is a good option where, if you really like the home, or the deal is that good, doing the repair (with permission) is worth it.