The cursor in the CD version of LotR 1 is a bit laggy, e.g. when scrolling down, it takes a bit of time for it to respond when I move up, making it a bit difficult to move around the map.

Floppy version runs fine.

In addition to this, does anyone know how to bypass the intro and credits when you load the game. Or are you forced to go through it every time with many clicks?

In fullscreen the game's original resolution of 320x240 is scaled to 640x480. The mouse still seems to behave like on your desktop resolution. Thus it's to fast and a bit imprecise now. You could try setting your desktop to 640x480 or slowing your mouse down in it's control panel. The mouse acceleration usually results in smoother mouse movement here. As such a low desktop res is annoying for every other task and if it actually helps, I'd create a new account just to play the game and set the resolution there.

Skipping the movies is easy:
Just got to ..Lords of the Realm - Royal Edition\Lords of the Realm I (CD)\VAS
and rename the following files:
INT1.VAS
INT2.VAS
INT3.VAS
INT4.VAS

Thanks, but that's not the issue. I tried playing around with sensitivity already and it didn't help much. I'm used to low resolution in old games, but this is different. It's not fast or imprecise, it's a bit jittery and erratic. As I said, the floppy version which uses the same resolution runs fine.

You're not the only one -
http://www.gog.com/forum/lords_of_the_realm_lords_of_magic_series/lords_of_the_realms_1_has_been_updated/post9

Solved! I'm posting here in case others have this problem too:

After a bit of testing around, I found out that the problem doesn't happen in the middle, left or upper part, but only in the lower and right part of the window.

The reason behind it turned out, that if you move the mouse all the way down, then you can still move it a few pixels lower. Even though the cursor appears on the last lowest pixel, in reality the game registers it to be lower than that. If you then move your mouse up, the game first moves it through those invisible pixels below the screen, before actually moving the cursor up.
Same thing happens in the right side of the screen. It doesn't happen on the left or top side of the screen. I suspect the reason behind it is that the cursor has its pointer in its top left corner, so if you move to the right, or bottom of the screen the pointer will still move through the width or height of the cursor.

This is especially problematic for two reasons:
_In the Kingdom view, you scroll a lot, scrolling right or down becomes a bit erratic.
_The bottom part contains the buttons in Kingdom view, so you move your mouse there a lot. The right part contains the buttons in County view, so you move there a lot too.

It works correctly in the floppy version.

Solution?
The solution is to restrict the cursor to the 320x200 window (the original resolution of the game).
You can do this using AutoHotKey, which is a free program.
http://www.autohotkey.com/
Here is a script to clip mouse movement:
http://www.autohotkey.com/board/topic/20345-protecting-an-area-of-the-screen-is-it-possible/#entry133444

Just make sure you edit the third line to
ClipCursor( Confine, 0, 0, 320, 200 )

You can also change the shortcut on the first line (the script in the example sets it to Ctrl+F2).

You will have to run the script every time you run the game, but you can set this in a batch file or the script itself.

If you need any further help on how to set up the script, let me know.