Online discussion moderators must make ad-hoc decisions about whether the contributions of discussion participants are appropriate or should be removed to maintain civility. Existing research on offensive language and the resulting tools cover only one aspect among many involved in such decisions. The question of what is considered appropriate in a controversial discussion has not yet been systematically addressed. In this paper, we operationalize appropriate language in argumentation for the first time. In particular, we model appropriateness through the absence of flaws, grounded in research on argument quality assessment, especially in aspects from rhetoric. From these, we derive a new taxonomy of 14 dimensions that determine inappropriate language in online discussions. Building on three argument quality corpora, we then create a corpus of 2191 arguments annotated for the 14 dimensions. Empirical analyses support that the taxonomy covers the concept of appropriateness comprehensively, showing several plausible correlations with argument quality dimensions. Moreover, results of baseline approaches to assessing appropriateness suggest that all dimensions can be modeled computationally on the corpus.