Andrea,
Welcome! While I don't have personal experience with the '07 SE Dyna, I have owned bikes with this same issue over the past 40 years and I fully understand your concern. I did a little searching on the 'net and came up with a post from a different site regarding your issue that makes good sense:
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"They are very much aware of the mirror vibration problem and are seeking a solution. It is caused by a combination of three factors - a very large stroked motor that shakes at lower RPM's - direct mount handle bars (no risers) - and slotted stem mirrors. They asked me to return my bike to my dealer and to have the dealer first insure nothing else was causing undue vibration (ie: wheel balance, motor bracket problem, etc) and if everything else was ok to then try different handle bar / mirror combinations to try and resolve the problem. They assured me that they would pay for finding a resolution to the problem. I'd suggest owners of the new FXDSE contact Harley Davidson Dyna Tech Department and discuss the problem with them. They will give you a Reference Number to give to your dealer with instructions for your dealer to contact them for detailed instructions on how to proceed.
At this point in time, HD does not want to do a full fledged recall as they dont think the problem is with 100% of the FXDSE's, but to instead handle the problems on a one on one basis until they can find out what is causing the excessive mirror vibration issue."
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This has been an issue on many different Japanese bikes over the years, enough so that the aftermarket has designed dampers that install between the mirror stem and the handlebar bracket to alleviate the shake. Unfortunately, those I am aware of have 10mm threads that only work with Honda/Yamaha/Suzuki etc. If I come across any designed for a Harley I'll post the info later.
Jerry