Good points, yes
Okay, some thoughts. On description for the FBI artist, wasn't it something like "hair sometimes curly, sometimes straight" and a height, estimated weight, etc? Pretty generic, but realistically, unless there is something particularly notable about a person's face, or something like a tattoo and etc., I don't think it is that easy to give a description that narrows down to matching only one person.
Suppose Casey lied about knowing Zanny for 4 years -- she might do that so as to make it sound like she had been responsible in terms of not letting some virtual stranger look after Caylee. She might have also lied about things like spending the night with the nanny, visiting in the apartment, and etc. for the same reason -- just to come across as being more responsible than she actually was about who was looking after Caylee. But suppose she did know a "Zanny" for 4 years, I personally do not believe it would be that hard for someone to keep up a phony persona that long -- not if it was important to them to do so. Maintaining a phony persona to someone who is not asking the Right Questions wouldn't be hard at all.
As for evidence of phone calls and the rest -- normally I'd be totally stumped on that, but we have Casey saying she had a second phone that she has lost (one way or another). Suppose Casey used that second phone for all her doings that she was lying to others about (such as where she really was at times when she said she was at work), for all calls and info in connection with the nanny (that she didn't want anyone to actually meet), etc.
Last but not least, this totally Hypothetical nanny may well not have asked much money from Casey in return for babysitting -- anything she could make off of babysitting is money under the table for her, and if she babysat for other kids she could be getting several hundred a week by only charging something like $35 a week per child ... such a cheap arrangement could be why someone like Casey might think it was such a deal that she didn't want to ask many questions and look a gift horse in the mouth.
Again, total speculation.