I noticed that whenever something new appears in the current level for the first time, it is loaded and the game stutters. I guess thats happening when you reach the first checkpoint/pickup in your video.
The solution would be to place everything (meshes, textures, particle emitters, sounds, …) that can appear in a level somewhere hidden, so that everything is loaded on level start and does not have to loaded on demand while the level is running.
But I don’t know what is happening at the end in the video (~30s), since I cannot make out any special occurences.