I'm surprised no one has mentioned it yet. Maybe they have and I missed the post.
But, his initial "sos" call was made while he had a perfectly functioning sailboat. It was holed, and he repaired it, didn't have electronics but, the boat was operational. I'm guessing he knew the general direction he wanted to go even without charts or electronics he could have sailed to safety. Why did he attempt his Mayday call when he did?.
Honestly I don't pick movies apart that much. They are made for a general audience, people who don't know proper radio procedure for instance.
I thought the movie was a bit slow, entertaining and thought provoking though. For instance, trying to figure out his back story. Was he running away? That sort of thing interests me more than what life jacket he was or wasn't wearing.
It's been almost a week since I've seen it so I'm not quite sure on the chronology. Anyway, even though he did patch the hole I personally wouldn't have had much faith in that repair and I believe it ultimately did fail.
Also after losing all electronic navigation aides, attempting to get some help seemed to be the wise course of action, especially since the radio was also only marginally working.
I actually thought it was cool that no back story was provided and you had to fill in the blanks yourself.