Can I hang a mezuza with velcro strips?
It can swing a little if you bump into it, but it doesn’t fall.
One should not affix a mezuza with velcro. Although it may be somewhat securely fastened, the nature of velcro is to be a non permanent connection, to easily come on and off. This type of fastening does not constitute sewing or building according to halacha, with regards to Shabbos. Using it for a mezuza which should be permanent is highly questionable and should be avoided.