It's not strictly speaking a bug, but the behavior of Advance is a bit confusing. Based on how you use it in the code snippets, I would suggest changing it to

private void Advance() {
    current++;
}

So that it only does what it says, and then changing the place where you read the next char to

char c = Peek();
Advance();

Alternatively, you could rename it to something like ReadChar, which more closely matches its current behavior, since a read is expected to return the data (character) at the current position, and then advance the position