When I tried to download V. 2.25 my security software indicated that the site was an attack site and, when it had been visited recently, it had featured several trojans and other malware.

Should that not raise any concerns? What's the story?

These are false postives. Based of what ccleaner does it will often report as a trojan to certain Antiviruses you should reprot this flase to the maker of the AV program. But always make sure to download ccleaner from either here or Filehippo and NO OTHER Places