Hi John,
I have faced the same situation on a number of occasions, candidates taking the offer letter and then using it to get into a better position in either their existing company or some other company.
While there is no way to avoid this, we have started following a slightly different system. First is I have included this clause (just for the sake of it) in the offer letter, "This offer letter is a confidential document only for your personal reference and stands revoked if it is revealed to any other person/company."
We know that there is no way we will know if the candidate is showing it elsewhere or not, but it does make an impact when highlighted in bold. The other thing we are doing is not issuing an offer letter till the candidate gives us confirmation that he is ready to join us and gives us a perfect joining date.
The last and final thing we do, especially when candidates have to fulfill a month long notice period is to have them sign the offer letter in advance. That way they can't really turn it down at the last moment. While it has not happened to us yet, I am sure that whenever it happens, I will definitely be in a position to take some action against the candidate if he withdraws after signing the offer letter.
These are just some ideas that we have implemented. I hope they help...
Regards,
Gaurang S