Re: soft spots?
Greetings!
With regards to your transom, presumably you have some access to it? With mine I could assume the rarely done Yoga position called "Broken in half Crane standing on head" and I could get to my Transom. If you can reach it with at least one hand in various places then that should be all you need to check.
Stick some tape on a decent sized drill bit about half as thick as your transom (make sure you aren't going to go all the way through it) and drill in various locations and see what color and consistancy shavings you get. All light-brown dry shavings = good. Dark crumbly damp shavings mean you have a lot of work ahead (but plenty of folks here can guide you).
As for the floor soft spot..well.. I don't know your boat really but I suppose I would be real tempted to peel back whatever carpet or decking was in that soft spot and see what I had going on there. If the plywood is shot like it sounds then get out a circular saw and set it to about the depth of the plywood (start shallow if you aren't sure) and cut a square in that section and see what you have underneath.
If everything is ok then at worst you have peace of mind and a only a small square to mend up that needed to be replaced anyway. If not, well.. you are probably still better off than me. heh
Respectfully,
-T
ps - post some pictures of what you find. Folks here like those and they might see something else that needs more investigation or attention.