I was in the....uh huh......same boat this year. I picked up an aluminum boat and trailer for $100. Before doing anything I wanted to make sure that the boat was good to go and make it look a bit nicer. I put a wire wheel on a corded drill and went over the whole boat especially the seams that had old chalking on them. I then got 2 tubes of UV4000 and did all of the seams and a few rivets where the metal had small cracks. After that I masked the seams about 1" either side and sprayed rock guard along all of the seams. I bought a quart of paint from Can Tire and sprayed the entire boat silver and then sprayed a blue stripe on each side with Ford blue from 2 spray cans also from Can Tire.
My seams look good and sealed and I'm confident that the boat won't leak. Hopefully, it lasts a bit. Total cost was about $100.
For your boat I'd definitely drill out and replace the broken rivets and use JB Weld for any larger problem areas (ie gaps, holes, etc) and then go through a similar process that I did. I wouldn't just do the problem areas, I'd do the whole boat. With my luck I'd fix one problem and another would appear and the next thing you know you are fixing it all of the time. Do the whole thing right the first time and be done with it. GL.
