I haven't come across too many savings myths other than the usual grocery store "always use coupons" and "buy generic" ones. Those aren't always true.
Also, in the case of credit card debt, to pay down the card with the lowest balance first. That will not always reflect the greatest savings.
Good tips. I'd add that it's often not a good idea to use just one bank. One may give higher savings interest and another could have free checking, etc. I guess it's that old "all your eggs in one basket" thing.