With due deference to FumbleFingers, the first sentence is fine if somewhat colloquial.
A) The next appointment to see the dentist is this Friday afternoon.
B) I can't wait to Friday. I need to see the dentist today!
I imagine the use of "to" here is a gradual phonetic shift from the more grammatically correct till which is itself synonymous with until. It would be more "formal" to say:
I can't wait till/until Friday.
Also, as FumbleFingers mentions, this use of "to" is not usually written except as a quote or as reported speech. Otherwise your second sentence is incorrect, and should instead be:
I can't wait for Friday (to come).
meaning that you are really looking forward to Friday.