I make 1-2 batches (14 bars per batch) of PT soap yearly.
A batch can sometimes have a mottled look. That doesn't just randomly happen for me -- it generally happens when I don't get the ingredients mixed together well enough, as Zany and Ali have also mentioned.
One reason for this mottled look is if the fat along sides of the bowl doesn't get mixed into the center portion of the soap batter. So I think it's important to carefully scrape the sides of the soap pot while mixing the soap batter right before pouring into the mold. Sometimes the temperamental nature of pine tar doesn't allow that to happen, so it's a goal to shoot for.
Also if I'm going to use fragrance or other additives, they go into the fats or lye solution before I start the soap making process.
Although I've tried a number of ways to make PT soap and they all work more or less, the method I like best is to divide the fats roughly in half. One half goes into the soap pot.
The other half and the pine tar go into a second bowl. Mix the PT really thoroughly into those fats. Then set that half aside.
Add all the lye solution to the fats in the soap pot (no pine tar in this half). Bring that batter to emulsion or very light trace as usual. Set the stick blender aside.
Pour the PT-and-fat blend into the soap batter. Gently, slowly hand stir the two together with a large silicone spatula, making sure to scrape the sides of the bowl as I stir.
Just as the glossy shine on top of the batter turns a little bit grainy or hazy, pour immediately into the mold.
This method usually gives me really good results.