Warnings are only useful if they're about something concrete and verifiable, like
--arrive on time and don't leave early --double-check the SKU before sending out the order --when a supervisor talks to you, stop what you're doing and give them your undivided attention --wear clean clothes
(just making things up there). If you simply want him to shape up, without any specifics, that's not likely to do any good.
How soon after hiring someone would you subject them to the possibility of a written warning?
Less than 1 microsecond. Once you're hired, you fall under all the company rules. Which, of course, should be well defined in the employee handbook.
I read this question from the other side. Sometimes new employees will be on probation for a while, meaning that you can dismiss them for any reason. It doesn't make a whole lot of sense to go through several months of warnings if it was obvious within three days that they're not going to work out.