How to perfectly combine clips
First, check to make sure that neither you nor the app have created handles on your clips. Handles are a few frames at the beginning and end of a clip that are used to overlap with another clip when doing a crossfade or other transition.

If you're sure that the in and out points of the clips really are the first and last frames of each clip, then you're probably out of luck. (See below for 1 possible solution.) Why does this happen? Without knowing the camera you used, I can only guess. There are 2 reasons that cameras will break clips into smaller pieces:


U.S.E.U. Tax Code - When importing a camera from another country, if the camera can record 30 minutes or more (I think - don't quote me on the exact time), then it is considered a video recorder and is taxed at a higher rate than a still camera. To skirt this issue and keep prices low, many low-end cameras will limit their record time to 1 frame less than the minimum required to be considered a video camera. Many will even automatically create multiple clips that are no longer than the limit. Here's a link that explains it
File System Limits - Older file systems (particularly DOS's FAT file system which is used by lots of cameras) may have a maximum file size limit of either 2GB or 4GB, depending on the implementation. If your clips are long enough to be bigger than 2 or 4GB, some cameras will split the clip into multiple files automatically.


So it could be the camera auto-split for one of the above reasons. The thing is that some cameras will drop frames during the splitting of files, and when they do, there's nothing you can do to get them back. You might be able to create in-between frames using a tool like Re:Vision FX Twixtor, or a similar product.