Toxicity labels at sub-document granularity and disaggregated labels lead to more nuanced and personalized toxicity classification and facilitate analysis. We re-annotate a subset of 1983 posts of the Jigsaw Toxic Comment Classification Challenge and provide disaggregated toxicity labels and spans that identify inappropriate language and targets of toxic statements. Manual analysis shows that five annotations per instance effectively capture meaningful disagreement patterns and allow for finer distinctions between genuine disagreement and that arising from annotation error or inconsistency. Our main findings are: (1) Disagreement often stems from divergent interpretations of edge-case toxicity (2) Disagreement is especially high in cases of toxic statements involving non-human targets (3) Disagreement on whether a passage consists of inappropriate language occurs not only on inherently questionable terms, but also on words that may be inappropriate in specific contexts while remaining acceptable in others (4) Transformer-based models effectively learn from aggregated data that reduces false negative classifications by being more sensitive towards minority opinions for posts to be toxic. We publish the new annotations under the CC BY 4.0 license.