A clicking or popping sound from the front of the vehicle (left or right side) while accelerating from a stop may be fixed by installing a rubber gasket on the axle shaft.Google+
Car Problem Reports
Dodge Neon Clicking or Popping From Front of Vehicle While Accelerating
Dodge Neon Problem
Drive Trains Affected: Automatic Transmission, Manual Transmission
Average Mileage: 90,571 mi (53,000 mi - 160,000 mi)
Vehicle makes popping, straining, squeaking sound... seems like it's coming from dashboard/front of car.
I get a slight clunk noice when starting forward and upon braking. Someimes I can feel it through the brake pedal. Not a major noise but worrisome. Car runs fine otherwise.
Visitor, 2005 Dodge Neon, 70,000 mi
Same problem area. Clunk/pop noises when starting forward or braking.
Visitor, 2001 Dodge Neon, Manual Transmission, 160,000 mi
Makes a popping noise while accelerating on freeway / freeway speeds. Does not occur frequently seems to just happen randomly from time to time
Visitor, 2003 Dodge Neon, 115,000 mi
Popping noise when braking and accelerating just started
Visitor, 2003 Dodge Neon, 90,000 mi
when I excelerate at times not every time but some times I get a quick pop sound just 1 pop then it stops !