Can't confirm (as I have never done this), but it has been reported by others that as long as it is within the original 24 hour rental time, your account won't be be double charged.
Again, I can't swear to this myself and urge caution as Verizon billing can sometimes be a nightmare.
keyboards is exactly right. you can order it as many times as you want, on as many tv's as you want, as long as it is within the 24 hour rental period. It will look like you are ordering it again but you will not be double billed. Just make sure that you are done with all watching by the end of the 24 hour period.
If you rent at noon monday, make sure that you are finished by noon tuesday. If you start watching at 11am tuesday and are not done until 1pm tuesday, THEN you will be billed a second time.