Some issues I've noticed with Finder:
1. Minimise a Finder window to the Dock. Right-click it. There used to be a "Close" item (something I asked Apple to put in back in 10.5, and they did). It's gone now, so to close a minimised window you now have to open it and close it from there.
2. Open two Finder windows. In one of them have an alias to a file in the other window. Select the alias and choose "Show Original" from the right-click menu. In 10.5 the item in the other window would be selected. In 10.6 the current window changes location to display the original file. You now have two windows showing the same location.
3. You can no longer start a drag-select action to select a bunch of files (in a list view window that doesn't have focus) by simply clicking and dragging into that unfocused window. You have to give the window focus before you can start the drag-select.
4. You cannot start a drag-select in a list view window on an item that is already selected. You have to deselect it first and then start the drag-select. If you don't, you end up moving the individual item you had selected.
5. You cannot rename an item if it has a period in it, without retaining the period and extension. For example, let's say you have an alias to an application, and you've put the version number on there, so "App v1.2.3". Try renaming it to "App v1.2.4". Finder renames it to "App v1.2.4.3" because it wants to keep the ".3" as the extension. You can only rename a file like this in the Get Info window. Productivity killer.
6. In a ist view window, click the disclosure triangles for some folders so that you open them to see their contents. Now, sort by one of the columns, say, Date Modified. Your folders are ALL closed. If you close and re-open the window, the folders are open as previously. It seems the window loses the states temporarily and a close and re-open restores them. Still, a productivity killer. I've created a simple video to show this:
http://www.youtube.com/watch?v=0IL8WwbDGk4
I've bugged all these with Apple. It looks like the new Finder is a step backward. Hopefully, 10.6.1 will fix some or all of these. Some are real productivity killers for me.