What influences the success rate for "errands" in Final Fantasy Tactics?

When just dealing with success or failure, the important points are as follows (see this FAQ in section 00err1):

Each character contributes a number of "Work Points" based on three factors:
 * Current job
 * Bravery & Faith
 * Exp Level

From the Final Fantasy Tactics page on SquareHaven:

To increase the success of any job, send the maximum amount of units (three). Also, some jobs can be performed best by certain classes or a certain type of class (e.g. physical or magic), which the bartender will sometimes allude to when the job's proposition is selected. (In addition, the correct type of job can be deduced sometimes by reading the proposition.) Specify the maximum amount of days. Finally, recall your deployed units when a job is completed as soon as possible.

So, try to deduce the proper classes to use, and follow the other guidelines you've already been using - send the max number of people, for the max amount of time. Maxing out the time doesn't appear to increase the odds of success, but it does help you to get the best rewards.

For more information, consult this FAQ, specifically section "00err2." There's a list of all the errands in the game, the jobs that they prefer, and some tips for each errand for earning "bonuses" based on the characters Bravery or Faith stats.