Place potatoes in a large pot of cold water. Bring to a boil and reduce heat to a simmer. Cook potatoes until just done about 15 minutes.
Drain potatoes well and let sit until cool enough to handle. Peel and dice potatoes.
Place potatoes in a large bowl and add onions, parsley and capers.
Combine vinegar, caper liquid and mustard in small bowl. Whisk in oil. Season to taste with salt and pepper. Pour over potatoes and toss gently. Let stand at room temperature.
Can be made 2 hours ahead of time.
Make the dressing ahead of time and refrigerate until you are ready to cook the potatoes.
Use potatoes that are roughly the same size so they cook evenly.
Cook the potatoes until they are just fork tender. Overcooking them leads to mushy potato salad.
Drain the potatoes well as any extra water left in the pan will be absorbed into the potatoes.
Go easy on the salt when you first dress the salad. Since both the caper liquid and capers add salt, you don't want to add too much salt at the beginning. Let the dressing absorb into the potatoes and taste again. When you are ready to serve, stir and add more salt if needed.