When I try to open a DMG file I get this:

I'll just transcript the image:

There may be a problem with this disk image. Are you sure you want to open it?

Opening this disk image may make your computer less secure or cause other problems.

What does that mean in fact? What's really wrong with it, and what kind of problem can it cause just by mounting?

Someone said:

When you download a file in Leopard (and Snow Leopard), it's marked as a quarantined file. This occurs by the OS adding an attribute to the file, tagging where it came from (such as "downloaded by Safari"). This is what causes the user to see prompts when running files that were downloaded from the Internet, you may remember being asked to confirm you'd like to launch program XXX downloaded by Safari on XXX date. As a new part of Snow Leopard, files which are tagged with the quarantine attribute also have integrity checked by fsck, and if that verify fails you will see the message you described, triggered by an unused node in the disc image.

But really, I didn't get that. What's quarantine? I've just downloaded a file here on SL, tried to open, and got that warning.

Apple have a say about quarantine files, and they seem to work the same on Leopards. Plus I have got that file using Google Chrome while that feature seems to work just with Safari.