Are there any issues when installing Arch Linux with an old ISO image? Generally all packages are downloaded from mirrors during installation, but I want to be sure.
It depends how old the image is. You should read the News on the Arch Linux home page to see what has changed since the image you are proposing to use. For example, anything older than October 2012 is pre-systemd.
Having said that, Arch is a rolling release and if you cannot readily obtain up-to-date installation media, then you will probably struggle maintaining it. If at all possible, download the current image and install from that.