when you first create a character and go through the new character tutorial you will have to talk to a surgical droid, go to a chest, get a pistol, blow away some boxes, and blast a security door, this will get you almost half of a level up and can be reapeted by:
simply log off before you get on the millenium falcon.
this will allow you to get extra xp and im not sure if the beginning tutorial before you get on tansari point station is considered tansari point station because you are only allowed to be lvl 10 and lower and if the beginning area is not tansari point station then you will be able to get unlimited xp.
the stormies that you have to kill will also drop ramdom loot anywhere from paintings to low lvl weapons.
also, you will be able to get unlimited issued pistols which are no trade items that you can sell to a junk dealer for money.
its not a major super xp grinding exploit but its an exploit.
