Well as many said, it might be the HD disks. Tho my experiance with amiga explorer and the a500 you will have trouble writing disks with less then 1MB memory.
Dont worry about your 1.3 rom, you will not need a 2.0 rom for many games, also as someone said you might need 1MB expansion to run alot of games, I dont realy think that is the issue because most games requiering 1MB to run will tell you that when you try to start them.
so get an memory expansion, clean your disk drive, try to get a hold of DD disks and try again.
also try formating the disks a few times and try to write the game that do not work again on another disk.