Yes, Barrel needs to be tightened more.

This is a common problem with M1's, M14's/M1Aicon's due to a lack of index marks on barrel and receiver.
With the M1, try to mount it in a vise or something so that the receiver is level, then push the gas cylinder, (without front sight) onto the barrel splines and place a flat piece of metal about 4" long across the top of the flat on the gas cylinder where the front sight attaches. If the barrel is indexed properly, the 4" piece of metal should be level. If it tilts one way or the other, adjust as necessary. There are many other measuring methods than the one described that also work and accomplish the necessary result. Use the one that you are most comfortable with.