Activity completion docs (http://docs.moodle.org/dev/Activity_completion_API) include setting completion of an activity to be dependent on one condition OR another, and that's partially implemented in the code, but the current GUI only allows AND, not OR.

As an example, as described in the API docs, one could say a quiz is complete
when they either pass or fail - if they get a passing grade OR use the maximum number of attempts. With the current GUI, this is not possible - the conditions are combined via AND, OR is not an option.

Several forum posts suggest a need for this to be completed, as do comments on a similar situation with conditional activities. (Conditional activities may have less need for OR if the OR can be done at the completion level.)