This list from the JMM 2013 Minicourse Teaching and Assessing Mathematical Communication characterizes effective presentations of mathematics majors.
Formal correctness: Definitions and terminology are correct; assumptions and givens are clearly stated; mathematics is correct; grammar etc. are correct.
Organizational structure: Good logical flow; structure of presentation (intro/body/conclusion) is clear; good outline or overview; attractive intro with brief background and good motivation; clear conclusion and summary of ideas.
Micro-organization: Appropriate detail, completeness and emphasis; good examples; avoids tedious details; appropriate mix of generalities and specifics
Preparation: Topic chosen is interesting and of appropriate difficulty; crafting of presentation shows awareness of audience; demonstrates comfort with own presentation, e.g., not just copying notes; appropriate choice of slides vs. blackboard.
Implementation: Audible, understandable speech; enthusiastic and interactive presentation; attentiveness to audience (notably, eye contact and pauses for understanding if appropriate); appropriate pacing; appropriate personal bearing.
