Is there any known danger of viruses associated with downloading the program? There's a warning that appears before allowing the download; and apparently, the download can come from one of many sites.
Good news. The answer is no providing you only download mIRC from one of the official mirrors which are all linked from http://www.mirc.co.uk/get.html - Just choose the location closest to where you live and download from there. mIRC is extremly popular which is why there are so many download mirrors.
Just in case: some virus scanners may give you what they call "a false positive" on mIRC even tho you have downloaded a safe copy from an approved site, so be sure you are current with their updates.