When Sara originally makes up the "contract" between herself and Joe, she does not sign her name on the bottom, writing only "One Million Dollars". Later on when Joe shows her the contract, her name is signed on the bottom.
There are many indications that the movie takes place around Christmas time, but near the end of the movie, as it is approaching 7pm (Texas time), it is still daylight outside, when it ought to be dark.
The legal goofs in this movie are hard to count, but to start with, in New York, the rule is that when serving process on someone all you have to do is mail it to them and tack it on their door. Sara running would have no legal effect.