One millisecond of previous clip gets stuck to next clip when inserting another clip in-between

It is kind of hard to describe but I hope you'll understand my problem. 

When I add a new clip in the middle of the sequence of my timeline (so in between two clips that were previously next to each other). A teeny tiny bit of the first clip gets 'stuck' to what used to be the second clip and becomes the third clip. So instead of changing a sequence of clip A-B to a sequence of Clip A-C-B I get; A-C-one frame of A-B. I thus have one millisecond of the first clip after the newly inserted second clip before the third (what used to be the second) clip starts. It is almost like I didn't cut the clips in the right place, but I never cut anything, I am using the clips in their full length. I hope this explanation makes any sense. Does anybody know what I need to do to stop this from happening every time I move stuff around?

*edit; the same happens when I move or shorten a title. The title will be visible for the amount of time that I want it to, but will reappear of a millisecond at the time it used to end before I shortened it.