In Lancaster the council have recently been tested gravestones for safety. A notice was placed in the local newspaper to this effect. A notice with a contact telephone number is then stuck on any gravestone which is found to be not safe. My Aunt found that one of our relatives graves was one of those deemed to be unsafe, she contacted the council and a stone mason and has arranged for it to be put right.
Yes, I would say it is normal for notices to be stuck on with duct tape and hazard tape to be stuck around them. I know it doesn't look very nice but once the gravestone has been found to be unsafe the people in charge don't want any accidents as they would then be in the position where they could be sued. In Lancaster the owners have (I think) 1 year from the notice being placed on the gravestone to get it sorted out, so the tape etc will not be around for ever.