I have a Dyna, but not sure if it is the S, I would have to check. I have ridden about 20k miles over the last decade with the Dyna in mine. I have never had to touch it. Much like yours, the PO had installed it. I found plenty of things that caused my bike (CB750 1974) to run poorly including poorly cleaned and jetted carbs, dirty plugs, bad connections in the spark plug wire caps. The usual suspects.
Some have reported problems with Dyna ignitions. In fact, some people get rather animated when discussing the merits of various ignitions. Having never owned a bike with points, besides an ancient Lambretta 150, I have to say that I don't know much about maintaining points based ignition systems, so I don't comment too much on other ignition systems.
I don't know how long the Dyna had been there prior to that, but I can verify that it has been in place since before September '99 when I purchased the bike.
Take that for what it is worth, but I would check some other areas of the bike before I worried about the Dyna ignition. My recommendation is to check the ignition wires for loose connections then check the plugs and replace them if they are questionable. Use the proper plugs for your wires. If the stock wires are present, they have resistance built into the caps. In that case you need non-resistor plugs. If all that looks good then consider running some Sea Foam through the fuel system to see if the miss clears up. This is also frowned upon by some, but has worked for me.
Best of luck and keep us posted with regards to your progress and failures. I learn as much from my failures as I do my progress, but the failures usually cost me more!
Luckily we have this forum. A place where we all learn together and sometimes avoid the costly mistakes by seeing what others have accomplished!
You have come to the right place for help. Welcome aboard!
Kirk