The thing to remember is to accect nothing less than perfection, otherwise you will be asking for poor groups and tuning problems.
There are 3 main ways to test:
1. Most preferred is to use an arrow spinner. This is a $30 purchase that you will use many times a year for many years.
2. Roll the arrow on a small table and watch for a wobbling tip. This can work but a moving wobble is difficult to detect.
3. Put the point of the broadhead on a fingernail on one hand with the arrow almost straight up. Cradle the arrow in the V made with the nails of your thumb and index finger of the other hand to minimize friction. Blow on the vanes to get the arrow spinning fast. You'll feel and possibly see vibration from an out-of-alignment head. This can work well, but it is pretty hard to detect minute alignment problems.
As for fixing a problem:
Try tightening the broadhead just a bit more and then retesting it. This works maybe 1 in 4 times or less.
Put another broadhead on that arrow and test. This works maybe 1 in 3 times.
Get some broadhead O-rings made for spacing the head in a different place on the threads. You can test, adjust tension, test, adjust tension until you find the spot that it is perfect. This works maybe 1 in 1.5 times.
Last, you can use a small drill bit inside the arrow and swing the arrow to knock out the insert and glue another in. Make sure that you have plenty of safe space for this because it will come out violently. This works most of the time, but you may have to go through the above fixes with the new insert.
Good Luck!