When SEO experts claim they can get someone’s new blog onto the first page of Google, what are the gotcha’s they are leaving out?

You have to beware of companies boasting this. Anyone can get you to the first page of Google for a keyword phrase that no one searches for. The real worth you have to look out for is how many goals are reached (newsletter sign-ups, sales made, etc.) when compared to the same month one year ago. Rankings can help that but you should beware of what you are ranking for and if they are effective and how many times they are searched for.