This error has been frustrating me for the past month. I finally called Apple support today and they told me to do the following - and it worked!!
My issue was downloading episodes from TV show seasons that I had purchased. When restoring my iPad Air, I had to leave the office and when I arrived at home, I found that all of my pending downloads now said "download error: Tap to retry". Tapping on the arrow of couse, did not work.
- go to the iTunes store on your iPad or iPhone
- click on 'purchased"
- find the tv series or movie that you're trying to download
- click on the cloud icon
- your download will resume
Be sure that when you set these items to download that you stay in the same wifi zone long enough for the download to complete.
Hope this helps someone!
Sandy