I exprienced a weird thing with a shortcut.

I had a shortcut in a folder (that folder's shortcut is on the dock that opens as a menu, in the menu I can reach the shortcut which im talking about).

It is a webpage shortcut to a webpage search result. After a while I wanted to exchange it to another shortcut to the same webpage with another search query.

After I dragged the shortcut to the same folder nothing happened, the shortcut remained the same.
When I deleted the shortcut, and after that I dragged the new shortcut to the folder, and I checked it, it behaved as the previous deleted shortcut.

I deleted it again, and I changed the shortcut in the explorer itself.
If I run the shortcut from the explorer itself, it behaves normally.
If I run it from the dock, it behaves like it was the previous deleted shortcut.

Does the dock run this deleted shortcut from a cache, and it doesn't check that it is a 'living' item or not if it has the same name than the previously deleted shortcut?

Actually, I'm not experiencing this problem at all. I can make any shortcut to anything (programs, documents, web pages/searches) and they all work fine.
What I could think of is that you may have dragged the wrong shortcut, or you have created a wrong shortcut...
What I suggest you to try (so we'll see if this is a bug) is to delete both shortcuts, and recreate them with the correct web link. Then try from explorer and see if they work, then drag'em both to the dock or shelf and run them from there. if they work now it means that you've miss dragged the shortcuts before; if it doesn't work it might be something else.
And last thing, are you using a 64-bit version of Windows? And which web browser are you using?

Have you checked the url that is specified in the items properties? Right click the item and you can check whether the URL is correct.

If the URL is correctly stored in the properties, then it is a bug.