I recently got a flat too....when they were balancing the wheel, they called me over to talk. The rim was bent....there is a little vibration at high speeds, but they were successfully able to balance it correctly
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simple put the rim on the wheel balancer and watch the run out..
you'll see real quick or can put your hand on the rim and feel any run out or bends.
a bad tire cannot balance too i've seen $300 tires from the factory impossible to balance.
I assume they used a hunter roadforce balancer. If not spend more $$ and go to a real tire shop. seriously. pep boys has them around here now. they score your rim and tire combination to give you the best possible ride.
Since this is what I do all day, I thought I would put in my $0.02 here.
There are four major causes of vibration at speed; rims, tires, alignment and suspension. Bent rims or out-of-round tires will generally cause a vibration at a certain speed range, as the vibration modulates into the suspension. Bent or misaligned wheels will also tend to cause irregular tire wear which can make the problem worse. Bad bearings, rotors or CV joints can cause vibration issues also.
A bent rim cannot be balanced correctly. While a good technician can make the assembly "zero out" on the balancer as if it is truly balanced, the balancing computer is assuming that the wheel is straight, so that if it is not the math, and therefore the balance, will always be wrong. This is not generally an issue of honesty or dishonesty, but that most tire techs do not know that bent wheels will not balance correctly, and that balancing a bent wheel will not correct the vibration issues.
Hub-centric rings are a necessity on aftermarket rims where the center bore is larger than the car's hub, as it is the center bore of the rim that actually holds the weight of the car. Driving without hub-centric rings will often cause vibration, as the lugs cannot hold the wheel entirely in place, and an impact can easily damage the center bore of the wheel, which cannot be repaired.
Mrkrad is absolutely right that the best way to tell if your rim is bent is to spin it manually on a balancer and look at each side. If you can see the outer edge of the rim move up and down or side to side, the rim is out of round. However, one must also make sure it is the rim and not the tire that is moving. We see customers all the time where a tire tech told them the rim was bent when it was actually the tire that was flat-spotted or otherwise showing irregular wear. Again, this is generally an issue of knowledge and experience rather than dishonesty.
Bent rims can often be straightened, in fact Rim And Wheel Works has been straightening aluminum alloy wheels for over 15 years. We use a proprietary process involving heat and hydraulic pressure to straighten rims to within .030", which is within factory specs for nearly all OEM and aftermarket rims. The process is both safe and effective, and usually much less expensive than the cost of replacement.