1. There is a tremendous amount of humidity inside a greenhouse that can affect a wooden greenhouse dome. I would coat the wood, even the ends of the wood, with something that makes the wood absolutely impervious to rot.
2. The water from the outside can seep into twin wall polycarbonate fluting between the panes and lower the light transmission. I would seal up the ends of the poly wherever possible. If you are using clear panes, that won't be a problem.
3. I might use large rubber urethane stripts or something like what they use for a car windshield and put it completely over the wood and under the panes to help keep out the water from the outside. Then I would fill the gap full of caulk and put waterproof tape over the gap between the panes. And I would replace the tape every year or so.
If you have a friend that is a contractor or professional builder, they might have a better solution.
Here are two fairly popular YouTube Geodesic dome builders that had some issues with their wooden greenhouse domes that might give you some ideas on how to avoid future problems:
John