Is it a bad idea to use other professors' Youtube videos as lectures?

The answer depends on your goals.

If you have plans to work in academia, eventually you might find yourself on a track to becoming a professor yourself. In this role, you are expected to teach. Hence, you should be able to prepare teaching materials of high quality to support your teaching and benefit students' learning. The sooner you start working on your first video lecture, the sooner you prepare the one which you are actually not totally ashamed of. Your first lecture might be half-baked and otherwise of sub-par quality, but that's expected on your career stage, when people start learning the ropes. But if you listen to feedback from your students and your mentors, and reflect on it, then your second lecture will be better than your first one, and eventually you start producing good quality stuff. Most importantly, you will become a better educator yourself, equipped with a wide range of tools and techniques, and understanding which method works best in a particular situation. You will be able to adapt your teaching to the needs of a particular student cohort, and you won't depend on materials from the internet (which may or may not be available).

But maybe your goal is simply to survive this teaching assignment until you graduate? In this case there is probably no shame in using online materials to complement your teaching. Just don't forget, that you still need to support your students and help them contextualise and understand the content. You may achieve this by preparing some examples based on the materials in the lecture and working through them with your students. It may be appropriate to have a discussion regarding the material, or even to critically assess and compare the material presented by different lecturers.

Good luck.

I am wondering if it would be appropriate for me to assign Youtube videos as lectures? Or would this be considered unprofessional/frowned upon/likely not allowed?

My short answer: No, this is not unprofessional or inappropriate. Give your students the best materials that help them understand the content.

If someone else puts something in an easy-to-follow or especially interesting way, I think that is a good thing to share. You did the back-end work to find that perfect thing, so sharing it is the natural outcome of your research. We (nearly) all use published materials to assign for students to read or work from, and nobody expects you to retype well-worn material in your own words to disseminate to your class. In fact, if anything, there is sometimes an opposite expectation that you use published texts as the primary content materials.

I think you should find the videos that you think are great and then start getting practice making your own. Maybe set a schedule where for every two videos you use from other people, you make one of your own. I think your students will want to hear from you in your own voice, because they know the examples you go over will probably be most like what they will expect to know for exams, etc.

Are there any pitfalls I should be aware of?

• The video could be removed by the owner.
• The video might take a non-standard approach to something, so you'll have to vet them carefully.
• Students might complain that they don't like a variety of different methods/people/etc. (if you are cobbling together videos from whomever).
• The videos aren't captioned appropriately (or at all) for accessibility purposes.
• You don't get practice making and posting videos, and something happens at the last minute where one of your videos doesn't work for some reason.

In normal (pre-covid-19) times, giving lectures is an essential part of the job description of a university course instructor. Planning to teach your course in a nonstandard way that involves not giving lectures without prior approval from your department is something that would have been almost certain to get you into trouble, and to reflect very poorly on your professional judgment.

During the covid-19 pandemic some institutions are getting more tolerant about alternative teaching arrangements, so your chances of having your department consider this sort of thing are a bit greater, if you propose a thoughtful plan that shows convincingly that students would benefit. Nonetheless, the fact remains that in the US higher education context I am familiar with, even these days “teaching a course” is assumed to be more or less synonymous with “giving lectures”. So again, planning not to give lectures means you plan to do things significantly differently than the norm. Therefore even if you think you have good reasons to do so, given your lack of experience and low ranking on the institutional totem pole it would still be pretty inappropriate to carry out such a plan without prior consultation with and approval by your superiors, and likely to result in negative consequences for your career as a graduate student.

TL;DR: it’s certainly a bad idea to do it without explicit approval from your department. The saying “it is better to ask for forgiveness than for permission” does not apply in this situation.