Elmer's purple school glue gave you problems cleaning the print plate? Just a little water and it softens back up and cleans right off!

If blue tape let loose, either 1) it was an elcheapo brand, or 2) you didn't clean your glass well enough first.

If you want something that absolutely will not let go (and you better not have your extruder set too close, or it really, REALLY, will not let go), try some BuildTak..