Hi,
From where are you dragging in the clips and what steps are you following to do it? What format are the clips that won't drag in?
The first thing to try is to delete preferences to rule out that a corrupt preference might be causing this misbehavior. To do that in iMovie 10, restart your computer and open iMovie while holding down the Option and Command keys and selecting to delete preferences in the box that appears. iMovie will open in a new library. Reopen your old library to get back to your project. Now see if you can drag in the video clips.
If still no luck, to rule out that the issue might be confined to just this one project try creating a new project and see if the clips will drag in there.
If the clips still won't drag in, try using the import button in iMovie (the down arrow in the upper left of your screen).
Also, check the format of the clips. You can try using the free download, Handbrake, to convert them to a supported format like Mp4/AAC and then see if you can import them.
-- Rich