Yesterday I did a backup of my data, and then ran chkdsk; although it said no errors had been found, now Ubuntu does mount the disk! Well, I'm not complaining
I will send a donation right now. Thank you very much, Fiona!
I have proceeded as in http://www.cgsecurity.org/wiki/Advanced_FAT_Repair#Rebuild_a_valid_FAT_boot_sector, writing the boot sector after checking I could see the data.
Now everything looks good (I attach the log file), and the USB disk seems to work fine with my Mac :) but it still doesn't mount on ...
I'm running TestDisk from Linux on a single-partitioned FAT32 1TB USB HDD which I used to share data between Linux, Windows and Mac. Now it's not mounting on any system.
Test Disk detected the original partition as duplicated:
Current partition structure: Bad MAC partition, invalid block0 ...