Web links as icons on iPad

I like to create web links as icons on my iPad (using "Add to Home Screen" in Safari). Today, though, I found a few of my older ones where the URL is no longer valid and so I was trying to get rid of them.

I press on the icon and hold till all the icons begin to wiggle with the little X in the upper left corner. However, if I tap the X on something I want to delete, instead of deleting, the icon along with random other icons on the same home screen start flashing to appear and disappear. All the icons retain the X in the corner but their rate of "wiggling" slows down.

Pressing the Home button does nothing to change the situation. The only way I could stop it is to reboot the iPad or attempt a reset.

Another anomaly that occurred today is that my web link icons all took on a generic appearance of white with a black grid. I have only been able to restore the original appearance of some of them by using them to access their URL - sometimes when the underlying URL fully loads in Safari, the link icon will pick up an image, sometimes it won't.

Thanks in advance for any suggestions on how to resolve this.