Wheel / tire problems

DStudstill

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Mazda 6 SportWagon
I had a flat and decided to purchase two new Yokohama Avia to match the fairly new other two. (OEM 17" wheels). Mavis did the install and the balancing was not correct. After two tries I took it to a Mazda dealer. They said the balance was way off and Mavis had broken a wheel stud. After the repair the front still vibrated slightly at highway speeds. I took it back to the dealer and they said there might be a slight problem with the tires and rotated them to the back. After the rotating and after driving 40 miles I hear a shudder like an out of balance washing machine. I pull over and check the wheels and three of the lug nuts on the left rear (one of the new tires) were loose. Also one of the lug nuts on the left front was a little loose. So my question is: -- Could a bad tire or something else other than improperly tightened nuts cause the nuts to loosen? Also -- Can locking nuts cause a wheel that has been balanced properly on the machine to be out of balance on the car? Thanks for your advice.
 
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