As some others have mentioned, it could be dirty heads in your floppy drive, so ANY Amiga user still trying to use floppy disks MUST get themselves a drive-cleaning kit. These things are usually just a disk with a scrubbing pad inside them that you drop a little bit of cleaning alcohol on, you insert it and let the drive try to read it a few times, and then the heads are cleaned. Once I put one of these disks through four of my Amigas, it fixed all the read error problems I was getting. I use HD disks in all my Amigas and don't have problems with them, although it wouldn't hurt to try writing each disk twice or three times so the image definitely burns in. Don't worry about covering the extra hole with sticky tape, as only HD drives have a problem with HD disks formatted as DD, and since the A500 is DD the drive doesn't have the hole-checking mechanism. Some newer A1200s and A4000s do, but no A500s.
Also, when you get a game that comes up with a cracker screen, you generally just have to click the mouse buttons to skip past it and get to the game. Many ADFs that you download will be cracked, and they generally have these little demo/scrollers at the start, sometimes followed by a trainer for unlimited lives and other cheats. On nearly any crack, clicking the mouse button (or the fire button on player 2's joystick) should get you into the game.
If your A500 doesn't have that extra 512k trapdoor memory, you definitely need it! It's probably the reason most software isn't running.
Head cleaners don't solve major problems like alignment. Rewriting disks doesn't do much to reinforce patterns on the media. On floppy drives, you can't guarantee being able to rewrite directly over the exact same spots on a track as far as I know from reading the RKRM manual I have which describes some of the process. HD media isn't reliable on amiga DD drives, it's hit and miss.
