There are many variables in the teaching/learning of a foreign language. As the previous colleagues have pointed out instructor's fluency and use of idiomatic language in classroom can be a challenge for a non-native speaker/instructor. Assuming the instructor is a non-native speaker, the challenge also lies in a shift of a focus from instructor's own linguistic competence/performance in classroom to students' in order to promote a learner-centered approach. This transition can be challenging for instructors (native/non-native) if they lack a supportive community of practice (with other instructors) that can promote a reflective practice and dialogue.
The challenges are too many to insert into such small space, but I'll mention one: that of getting shy students to speak and share their thoughts in EFL classrooms.
In countries where English is taught as a Foreign language, e.g.: Afghanistan, the key challenges the teachers face are the phenomenon of large classrooms and multi-ability students.
In my country, the challenges facing the English teacher are related to the teacher himself in terms of preparing him to be a successful teacher as many of our English teachers lack the qualifications for success. The other is the difficulty of accepting many students to study as a result of the use of inappropriate methods in education, and more importantly The whole nature of the examination questions (such as MCQ, True$False), from which the student can not learn the language
In language classes, as you rightly observe, there are many challenges influencing the attainment of course objectives. However, by applying cooperative learning, teachers should find effective ways to enhance learner cooperation by tightly structuring the class activities. By finding the right balance between teaching modes, tenets of philosophy of education, and students' preferences, teachers can encourage them how to cooperate, compete or adopt a self paced plan of action. By applying tiered tasks and bias tasks , teachers are able to deal with the problems arising out of students heterogeneity where both weaker and stronger students make the best of their class time.