I caught a nail in my tire, stock rim and tire, so I had them patch it up from the inside. After he mounted the tire on the rim, he did place the wheel on the balancing machine. I noticed he only put a 7.25 weight on the rim, where as before it looked like their were 2 blocks consisting of 6, 7.25 weights. I know because of the sticky residue.

Is their anyway I can tell that the wheel is not balanced? It's mounted on the front right side.

 

Take it for a drive and see if it's any worse.

It's possible that he turned the tire around the wheel, changing what needed to be done to get it balanced.

 

When they pulled the tire off the rim to patch it they changed where the weight was distributed on the tire. It was also slightly altered by the patch. Take into consideration that no rim is perfectly shaped, there are always minute flaws that can lead to uneven weight distribution. When balancing, if they used a sticky weight, they used a static balance. Which means they should have used a weight close to the inside of the spokes or what have you and then another on the far inner edge near the outside of the rim. If you get vibration after a certain mph like 30 lets say, then more than likely the wheel balance is off. But if not, being slightly off balance will not cause severe damage.

 

If a tire on the front of your car is unbalanced, at highway speeds you will notice your steering wheel vibrating. If it's your rear, you can kind of feel like your butt is moving back and forth in the seat. (that's the best way i can describe it..)

Where was the nail? If it was close to the side, you might consider getting a new tire. If the nail was beyond the tread groove/line of the tire near the sidewalls it should not be patched.