Mobil 1 will have lower viscosity at low temps, higher at high temps, than dino oil, so I suspect you have crud in the oil passages, along with some wear in the adjusters. The thicker dino oil masks the wear in the tappets at low engine temps.
If it bothers you, stay with the dino. If you want to change, you will need to run the Mobil 1 for about 1000 miles, then change it and the oil filter, the filter and oil will be full of crud that has dissolved.
The lifter noise may go away with extended use of Mobil 1.
I had rather severe lifter rattle in the 300D, but new o-rings on the oil filter shaft and some miles on Mobl 1 15W50 cured it.
By the way, if you have an oil filter canister with a long shaft that goes from the lid down to the bottom of the canister, check for the presence of two small o-rings toward the bottom. If they are present, change them (they are not in the oil filter box). On the diesel, these hold oil in the lifter gallery, and when they leak, the oil drains out overnight, leaving you with noisy lifters. Won't happen nearly so much with dino oil, it's thicker cold.
1972 220D ?? miles
1988 300E 200,012
1987 300D Turbo killed 9/25/07, 275,000 miles
1985 Volvo 740 GLE Turobodiesel 218,000
1972 280 SE 4.5 165, 000 - It runs!