Slipping is when the RPM's go up,and the MPH doesn't. It feels like the engine revs up slightly,but the truck doesn't go faster. It will usually happen in OD,with the torque convertor locked up. When you lightly accelerate the torque convertor lockup clutch slips because the pressures are low at light throttle. It usually happens when the power gets turned up from stock. It can also be accompanied by a vibration,as the clutch slips and chatters. Mine does anyways.
Your vibration could be a number of things. Start by checking the driveshaft carrier bearing and u-joints. If the u-joints start to sieze up and get rusty,it will cause the vibration you describe.