Before adjusting any offset on the radar, I would make sure that the amount of offset is ALWAYS the same. The issue isn't likely your radar, but rather the data on the mapping being fed through the GPS. If you have the radar on in clear weather, you can see what the radar sees... is it exactly the same as what's on your chartplotter? Likely, not.
I have seen people complain that their "GPS isn't working, because it shows us on land in a narrow channel." More likely, the GPS is working just fine, but the mapping data in that area isn't perfect. Many places haven't been resurveyed in decades.
The radar overlay is great to be able to tell if there is an obstruction ahead, or if that is a nav aid. Something HUGE on the water or the shoreline. You need to be able to trust your navigation equipment, but it is very important to understand the limitations of the mapping. Run the radar as you pass a nav marker: does it show up at the proper distance to starboard, then directly abeam, then quartering behind you? Turn around and make a pass the other direction and see if it is the same on port. If so, the radar is accurate. Run that same path with the GPS/chartplotter and see if it is accurate. Of course, to be accurate, you'd have to do that every place you cruise.
I have not run into a radar situation where there was an issue with an offset, but have frequently seen inaccuracies with the mapping. Nature of the beast. For me, being able to see the radar return in the approximate area where a marker is on the chart lets me know that it is that marker and not some other obstruction, like a boat. In low visibility situations, I am not going to be running so close to anything that shows up on radar that the discrepancy between the radar and the charting would make a difference.
Running two separate chartplotters, I have also seen different mapping representation in a given area. Most often, the mapping information will be "good enough" to guide you through an area... but when the visibility goes down, I want to know that I can trust the radar.