Corrected entry: The nanny said it was cold out and she was sorry she hadn't worn a jacket the day she was kidnapped; it makes no sense then that she was wearing sandals that day too.
Correction: We never see her feet, there is no way to tell if she was wearing sandals.
We can see she is wearing thong sandals when she is kneeling down by the stroller in her flashback to the abduction.
Correction: Unusual but not uncommon, and certainly not impossible. Many babysitters/nannies wear sandals while working no matter what time of year because 1) sandals allow them to be comfortable and 2) they are easily removed when entering the house so as not to track dirt, mud, or other harmful substances onto the floor where a child may be playing or crawling.