If Iam going to open an escort service, what are some basic legal issuesthat Ican expect running this business legally?

That is a very dangerous business to open. Note that even if you do not run it as a prostitution ring (and many escort services actually are), if any of the escorts take it  open themselves to offer sexual services in exchange for  money or other compensation, you could find yourself liable as their employer--even if  you end up being vindicated, you could have damage to your reputation, spend money and time defending yourself, etc.

As a practical matter, before doing something like this, if you have not already, try to  meet and speak with owners of other such services (presumably in different locations, so you're not competitors) and find out from them what the issues are--there's no substitute for  experience.

As a general matter, any high-liability-risk business should be set up as an LLC or corporation, so your personal assets better insulated from liability; you should maintain more-than-adequate insurance; you should written codes or expectations or rules of conduct which you have employees countersign and which you enforce, so as to make it plain you do not tolerate, let alone encourage or participate in, illegal behavior; and you should have an attorney *thoroughly* research ALL relevant laws (including any applicable zoning laws) and also look into whether cases have been brought against similar services in your area and on what grounds, so you can learn how best to avoid criminal or civil liability.