Pick a post that needs editing: You can use SEDE queries to find them, but there are only 14 left on Stack Apps and the list is below.
If the post still needs fixing, Use the "Wayback Machine" (Internet Archive, henceforth "WM") to recover the old the missing image(s) for that post.
If the WM says that the URL you tried is not stored, use a different URL. Every post in question is in the WM.
A good URL to use is the one you get redirected to after clicking one of the links below. For example:httphttps://stackapps.com/questions/1047
httphttps://stackapps.com/questions/1028/why-does-the-api-lack-proper-http-cache-control-headers/1047#1047
Use the WM tools at the top to go back to the earliest capture (in 2009, 2010 or 2011).
Two-thirds of the time, the desired images will be present. If they are, edit the post (from step 2) and use the image tool (CtrlG) to upload the image to Stack exchange's imgur account and insert it in the post. Delete the ImageShack spam.
If you can't find an image, edit the post to delete the ImageShack spam and leave an HTML comment in its place as follows:
<!-- Unrecoverable image. Tried: http://web.archive.org/web/20110429203340/httphttps://stackapps.com/questions/1203/how-to-order-sites-result-in-a-user-friendly-way-to-use-it-in-our-apps/1214 -->
- Done!
stackapps.com/questions/531stackapps.com/questions/531 - Done!
stackapps.com/questions/651stackapps.com/questions/651 - Done!
stackapps.com/questions/948stackapps.com/questions/948 - Done!
stackapps.com/questions/954stackapps.com/questions/954 - Done!
stackapps.com/questions/979stackapps.com/questions/979 - stackapps.com/questions/1047stackapps.com/questions/1047
- stackapps.com/questions/1115stackapps.com/questions/1115
- stackapps.com/questions/1162stackapps.com/questions/1162
- stackapps.com/questions/1214stackapps.com/questions/1214
- stackapps.com/questions/1262stackapps.com/questions/1262
- stackapps.com/questions/1289stackapps.com/questions/1289
- stackapps.com/questions/1338stackapps.com/questions/1338
- stackapps.com/questions/1344stackapps.com/questions/1344
- stackapps.com/questions/1377stackapps.com/questions/1377
Thanks so far to Nathan TuggyNathan Tuggy for his help.