Could minoxidil be causing the corners of my mouth to twitch/buckle when I smile?

Minoxidil has an extraordinarily safe profile.  There are however rare case reports of some neurological issues due perhaps to the potassium channel effects.  Consider ceasing medication to see if symptoms improve.  If not visit a neurologist.

There there have been rare reported cases of neurological symptoms from minoxidil. The incidence is approximately 1 in 5000. Twitching from emotional stress is more likely. I would suggest visiting a neurologist.

I would need to know more and examine the area to really determine if it’s related or not. It is possible, yes.A few years ago Dermatologists from India described a new side effect from minoxidil - specifically a vibration-like sensation/tremor over the lips and around the lips. Given the similar to a rabbit, the findings have been previously referred to as  "Rabbit syndrome."
Interestingly, when the patients reduced the minoxidil to a lower dose of the standard concentration, the side effects ceased. I would need to need know more about your story to see if it fits the defintion of what has been described. I advise my patients with similar type stories to take a video when it happens and share it at their appointments.
Overall, it’s a rare phenomenon and one needs to keep in mind this may or may not be related to minoxidil use. 
REFERENCE
Nagar R. Rabbit syndrome because of topical minoxidil foam. Dermatol Ther 2015.

You report that you have twitching of the mouth on minoxidil; however the two are most probably unrelated.