Check your browser prefs and perhaps also the Disk Copy prefs (since your profile shows 10.2.x) and deselect any 'automaticaly open' options you can find. You should be able to save a .dmg file onto the hard drive. Where the source of the download gives the download file size, check that against the size show by Get Info on the downloaded .dmg; the stated download file size is rarely exact but any discrepancy of more than a few kB would suggest the download is being corrupted in some way.
If double-clicking the saved .dmg file results in the spinning beachball, try opening Disk Copy (Disk Utility in 10.3 and later) and use the File menu's Open Disk Image command to open the file.
